The groups, including Human Rights Watch, called at an press conference for the 2019 Bahrain leg of the F1 calendar to be canceled in response to a lack of investigation into Yusuf's claims. She says she was detained and beaten for speaking out against the race on social media, which the Bahrain government denies.
Amnesty International also posted a statement highlighting "the grim human rights record of the country," on Wednesday.
The rights groups have also urged drivers, notably Britain's Lewis Hamilton, to boycott the race, which takes place this weekend.
Neither Hamilton, the 2018 champion, nor any other drivers have publicly addressed the concerns. Hamilton is expected to compete in the first qualifying round Friday night.
His arch-rival Sebastian Vettel, as well as Valtteri Bottas, the Finnish winner of the season-opener in Melbourne on March 17, are also expected on the Bahrain International Circuit track.
Yusuf, a former Bahraini civil servant, wrote in the UK's Guardian newspaper that she had been
"beaten and sexually assaulted" since her imprisonment one week after the 2017 edition of the Bahrain Grand Prix.
She says she signed a forced confession after five days of incarceration, following beatings and threats of rape.
Yusuf said she and many compatriots see the motorsports jamboree as "nothing but an annual reminder of our suffering in our fight against tyranny and repression."
She says that "every moment" of her continued imprisonment "stains the reputation of Formula One who have abandoned their commitment to freedom of expression and allowed injustice to be perpetrated in their name."
The government of Bahrain says Yusuf's imprisonment is not related to activism around the sporting event, but rather to "terror offenses."
"At absolutely no point has Najah Yusuf been charged or accused of comments relating to F1. Ms Yusuf was convicted of serious terror offenses. At no point during her trial did Ms Yusuf's defence claim that her right to free expression, or to protest against the F1, had been infringed. Attempts to link this case to the sport are a retrospective and misleading attempt to subvert justice," reads a government statement received by CNN.
The government also said it has worked alongside F1 to "clarify" Yusuf's claims, and that "at no stage of this process has any evidence been forthcoming to support Ms Yusuf's claims, despite their ill-informed repetition."
In a statement to CNN, Human Rights Watch global initiatives director Minky Worden characterized Yusuf's terror charges as "a tactic we have seen for other human rights activists and journalists where they are called terrorists, jailed, and often tortured."
Formula 1's statement of commitment to human rights
pledges to "identify and assess, by conducting due diligence where appropriate, any actual or potential adverse human rights impacts with which we may be involved either through our own activities or as a result of our business relationships."
F1: 'Surprise' at demands
The coalition of rights groups, including Bahraini organizations, sent a joint letter to the President of the Federation Internationale de l'Automobile (FIA), Jean Todt, calling on the racing organization to send a "high-level delegation" to investigate Yusuf's case, and visit her and other prisoners of conscience in Bahrain.
A statement emailed to CNN from F1 expresses "surprise" that campaigners are "making public demands of Formula 1 to visit Ms. Yousif (sic).
"In recent discussions with campaigners these demands were never raised, indeed they were supportive of private actions and next steps we are taking, that we outlined to them when we met.
"We all agreed it would be unhelpful to comment further publicly at this time. We've kept to those commitments, in line with our commitments to respecting internationally recognized human rights everywhere, and engaging with promoters to ensure nobody faces punitive action over freedom of expression."
Worden, the Human Rights Watch director, said Formula 1 had a moral responsibility to oppose rights abuses involving Bahraini opponents of the race.
"Formula organizers should not look the other way while Bahrain uses the publicity and grandeur of the races while stepping up repression against people who oppose holding the race in Bahrain," she said in the press release.
The country's Ministry of Foreign Affairs last year told the Guardian
that Yusuf's allegations of mistreatment were taken seriously and had been referred to its Special Investigations Unit (SIU), and that her conviction was a "matter for Bahrain's courts."
He was quoted as saying, "all individuals in the Kingdom are guaranteed fair and equal treatment within the criminal justice system."
Previous cancellation amid unrest
The race was canceled in 2011, after Arab Spring protests engulfed much of the tiny island nation and centred on the city's famous Pearl Monument. The following year anti-government protests failed to halt the GP, which went ahead even as nearby streets were blocked by burning tires and trash.
The furor surrounding the 2019 race is the second recent case involving sport and human rights in the Middle Eastern island nation.
Last November, Hakeem al-Araibi, a footballer who said he fled Bahrain in 2014 following torture and won refugee status in Australia, was arrested at Bangkok airport while on his honeymoon after Interpol issued a "red notice" -- an international arrest warrant.
He languished in a Thai jail for three months before international pressure forced Thailand to relent and repatriate him to Australia. Bahrain has denied al-Araibi's allegations of torture.
Formula 1 is the world's most popular motorsport, attracting a global TV audience of over 490 million unique viewers in the 2018 season, according to its own estimates.
Editor's note: This story has been updated to include a response from the Bahrain government.