Martin, a four-time time-trial world champion and one of the most respected riders in the professional peloton, says he's "totally angry" and that a "double standard" is being applied to Froome.
Four-time Tour de France winner Froome, who rides for Team Sky, was recently found to have double the allowed level of the legal asthma drug Salbutamol in his urine on a test taken on September 7 during the Vuelta a España -- one of cycling's three Grand Tours -- which the 32-year-old went on to win.
The sport's governing body, the Union Cycliste Internationale (UCI), said the British rider was informed of an "Adverse Analytical Finding (AAF)" on September 20 and that an analysis of the B sample had confirmed the results of the rider's A sample.
"Other athletes are suspended immediately after a positive test," wrote Martin in a Facebook post.
"He and his team are given time by the UCI to explain it all. I do not know of any similar case in the recent past. That is a scandal, and he should at least not have been allowed to appear in the World Championships."
Froome, Britain's most successful road cyclist, who won his fourth Tour de France in July, said: "It is well known that I have asthma and I know exactly what the rules are.
"I use an inhaler to manage my symptoms (always within the permissible limits) and I know for sure that I will be tested every day I wear the race leader's jersey.
"My asthma got worse at the Vuelta so I followed the team doctor's advice to increase my Salbutamol dosage. As always, I took the greatest care to ensure that I did not use more than the permissible dose.
"I take my leadership position in my sport very seriously. The UCI is absolutely right to examine test results and, together with the team, I will provide whatever information it requires."
On Thursday, Froome tweeted: It's sad seeing the misconceptions that are out there about athletes & salbutamol use.
"My hope is that this doesn't prevent asthmatic athletes from using their inhalers in emergency situations for fear of being judged. It is not something to be ashamed of.
That tweet drew this response from Dutch journalist Thijs Zonneveld: "It's not about asthma, you know that very well. It's about the question if you abused asthma to take more salbutamol than permitted."
'Wheeling and dealing'
Martin also believes cycling has suffered a "major blow" in its anti-doping fight.
"Not only the public but also I have immediately the impression that there is wheeling and dealing going on behind the scenes, agreements are being made and ways are being sought as to how to get out of this case. Do he and his team enjoy a special status?" he wrote.
"We need a consequent and transparent approach by the UCI. What is going on here is inconsequent, not transparent, unprofessional and unfair."
Both the UCI and Team Sky did not immediately respond to CNN's request for comment regarding Martin's comments.
The UCI has previously said Froome was not suspended, but wanted more details from Team Sky and was investigating the case under the organization's anti-doping rules.
Under World Anti-Doping Agency (WADA) rules, Salbutamol is a permitted drug without the need for a therapeutic use exemption (TUE), but only at certain doses.
The levels of the drug in Froome's urine test were at 2,000 nanograms per milliliter (ng/ml) -- double WADA's 1,000 ng/ml threshold. The test was conducted following Stage 18 of the three-week Vuelta.
Froome was the first Briton to win the Spanish event and his success also made him the first cyclist since 1978 to complete the Tour de France and Vuelta double in the same year.
The Kenyan-born rider is the first to win back-to-back Grand Tours since Marco Pantani won the Giro d'Italia and the Tour de France in 1998.
Dr. John Dickinson, head of the respiratory clinic at the University of Kent,
has said athletes are more susceptible to asthma than the general population. During tests on Team Sky's cyclists, he found that a third of the team had the condition. Team Sky declined to say Wednesday how many of its cyclists suffer from asthma.
Dr. Dickinson told CNN World Sport's Amanda Davies that while inhaled doses of Salbutamol did not boost endurance performance, taking the medication orally could improve sprinting power performance.
Dr. Dickinson also said it was possible for Froome to argue his case successfully.
"With this particular drug, and also with the case of Chris, there are a few circumstances that might have brought about why his urine sample has come back above the threshold," he said.
"WADA say that an athlete can take up to eight puffs in a 12-hour period and up to 16 puffs in a 24-hour period.
"We've shown data that demonstrates that if you're dehydrated the concentration level can go above the threshold level and also if your metabolism is fast that can also increase the level.
"There might be a few pieces of evidence that Chris can put together which may explain why his level is above the WADA limit or he's acted within the rules."