Solo yachtsman Abhilash Tomy is stranded 3,200km (2,000 miles) off the coast of Western Australia.
His yacht Thuriya had its mast broken during a severe storm in the Indian Ocean.
He managed to send a message saying he has a severe back injury and is immobilised, unable to eat or drink.
Race organisers said Tomy was “incapacitated on his bunk inside his boat…. as far from help as you can possibly be”.
A French fisheries patrol vessel is sailing towards him and could arrive by Monday.
Two military planes, one from Australia and one from India, flew over the yacht on Sunday to inspect its condition, but crew were unable to establish contact with Tomy.
“He is injured inside the yacht so he can’t communicate further,” an Australian Maritime Safety Authority spokesman told AFP news agency.
The 39-year-old Indian Navy commander, who became the first Indian to sail around the world in 2013, is communicating using a texting unit, after his satellite phone was broken.
His boat, the Thuriya, is a replica of Robin Knox-Johnston’s Suhaili, winner of the first Golden Globe Race in 1968.
On Saturday, he sent a message, saying: “Extremely difficult to walk, Might need stretcher, can’t walk, thanks safe inside the boat … Sat phone down.”
Tomy has a spare satellite phone in an emergency bag, but he is unable to reach it at present.
An Irish race competitor, Gregor McGuckin, whose own yacht was damaged in the storm, has made repairs and is attempting to cover the 150km (90 miles) separating him from Tomy’s position.
Meanwhile, race organisers say a search and rescue plane is being sent to Reunion Island to help rescue efforts.
An Australian and New Zealand Army Corps (Anzac) frigate with a helicopter on board is also en route, but could take at least four days to reach the area, organisers say.
Friday’s storm whipped up 70-knot winds and 14-metre (45ft) waves, which also knocked down the yacht of another competitor, Dutchman Mark Slats, twice.
Most of the 11 competitors still in the race were further north and avoided the worst of the storm, organisers said.
The Golden Globe race involves a single-handed circumnavigation of the globe – a distance of 30,000 miles – without using modern technology, except for satellite communications, Competitors started from France on 1 July; seven boats have so far withdrawn from the race.