In a development which will increase domestic pressure on the Italian government to bring the two marines home, Massimiliano Latorre collapsed on Sunday but was reported to be recovering in a neurology unit in the Indian capital.
His daughter said he had suffered an ischemia, a blockage in the flow of blood to the brain which can lead to a stroke.
In a case that has badly soured diplomatic relations between the two countries, Latorre and fellow marine Salvatore Girone are accused of killing the fishermen while serving as security on an Italian-flagged cargo ship off the southern Indian state of Kerala in February 2012.
They say they mistook the fishing boat for a pirate vessel and only fired warning shots.
Latorre was visited on Monday by Defence Minister Roberta Pinotti, whose decision to make the 16-hour round trip reflected the depth of feeling in Italy over the fate of the two marines.
Pinotti paid tribute to the quality of the treatment Latorre had received from his Indian doctors. "We noted that without such a speedy and timely intervention the situation could have had very serious consequences," she told reporters.
Pinotti's flying visit put the story back on the front pages on Tuesday, with reports speculating that the ischemia could have been brought on by stress linked to what is widely regarded here as the unfair treatment the marines have received.
Latorre and Girone are barred from leaving India as long as the charges against them have not come to court.
Criminal proceedings against the two men were suspended in March when India's top court agreed to consider a challenge to prosecutors' jurisdiction in the case and a request for the marines to be allowed home pending its outcome.
India allowed the marines to return to Italy last year in order to vote but insisted on them being returned.
Italy maintains the two men should be tried on home soil since the shootings involved an Italian-flagged vessel in what Rome maintains were international waters. India says the killings took place in its territorial waters.
The spat led to Italy recalling its ambassador to India earlier this year, but the two governments have both since attempted to cool the dispute.
New Indian Prime Minister Narendra Modi had a phone conversation with Italian counterpart Matteo Renzi last month and said afterwards that a speedy resolution of the issue was in the "mutual interest" of both countries.