The soldier inadvertently crossed the border to the Pakistani side of the Line of Control, which divides the Indian and Pakistani-administered portion of Kashmir, said Colonel Rohan Anand, press officer for the Indian Army.
He added that the Indian and Pakistani militaries are in talks for the soldier's release.
The arrest comes at a rocky time for India-Pakistan relations, in the wake of cross-border clashes that left two Pakistani soldiers dead.
The two soldiers were killed along the de-facto border Thursday in what India called "surgical attacks" to foil a "terrorist attack."
Pakistan has insisted that no incursion took place into the territory it controls, saying there had only been an exchange of fire.
After an emergency cabinet meeting
on Friday, the Prime Minister's office said in a statement that the cabinet "joined the Prime Minister in completely rejecting the Indian claims of carrying out "surgical strikes."
On Friday evening, the Pakistani leader's office confirmed it would convene a meeting of Heads of Parliamentary Parties on Monday to discuss the crisis.
The United Nations said it was "following this situation with great concern" and urged both sides to exercise restraint.
Bollywood films pulled
The latest flashpoint has unleashed a torrent of fury on social media and impassioned news coverage from both sides of the border.
On Thursday, The Indian Motion Picture Producers Association (IMPPA) asked that all Pakistani artists refrain from working on film projects in India.
Meanwhile, Bollywood films were being pulled in Pakistan. Nadeem Mandviwalla, owner of Mandviwalla Entertainment and shareholder in the largest cinema chain in Pakistan, told CNN that his theaters would temporarily pull all Indian films "until normalcy of relations between the two countries."
Nueplex Cinemas also joined the ban.
Indian Lieutenant General Ranbir Singh told reporters on Thursday the strikes had been based on "specific credible information" that militants were planning to carry out strikes in Indian cities, including Jammu.
"The operations were basically focused to ensure that these terrorists do not succeed in their design of infiltration and carrying out destruction and endangering the lives of citizens in our country," he said.
However, Pakistan's Prime Minister Nawaz Sharif condemned the attack in a statement, calling it "unprovoked and naked aggression" of Indian forces.
He said Pakistan's forces were capable of defending their territory and would stop any "evil design" against their country. "No external force has the capability or capacity to challenge the sovereignty and territorial integrity of Pakistan," he said.
Pakistan's Foreign Ministry said India's claims to have carried out surgical strikes were "baseless" and accusing India of "deliberately" escalating tensions.
The incident came less than two weeks after 18 Indian soldiers were killed in an attack by armed militants on an army base in Uri
, about 63 miles (102 kilometers) from Srinagar, the summer capital of Indian-administered Jammu and Kashmir. A nineteenth soldier was confirmed to have died Friday.
It was one of the deadliest attacks to take place on an army base in Kashmir since militant attacks began in the late 1980s, and sparked a furious war of words between India and Pakistan.
Long disputed territory
Kashmir, a Muslim-majority region, has been disputed territory between India and Pakistan for the past 70 years.
Both of the nuclear-armed countries hold separate parts of it and have fought two wars, in 1947 and 1965, over their claims. They came close to a third, in 1999.
Speaking to CNN on Thursday, a resident of Indian-administered Kashmir, Mushtaq Ahmad Chaudhary, said border residents had not forgotten the horror of having shells and bullets raining down on their communities.
"The latest developments have set in the fear and tension as the deteriorating situation may trigger cross [border] artillery duels [such as] we have witnessed during the 1990s when several villagers were killed and wounded," he said.