The six-time MotoGP world champion made a mistake on lap three after starting from pole position, wiping out home favourite Miguel Oliveira in the process.
"Possible fracture to 1st metacarpal in MotoGP rider #93 Marc Marquez's right hand," said MotoGP on Twitter.
"He will do a further examination at Dexeus hospital in Barcelona."
Honda's Marquez has also been hit with a double long-lap penalty for next week's Grand Prix in Argentina if he is passed fit.
"I apologise... This accident was my fault, I deserved to be penalised for it," he said.
If the fracture is confirmed, it would be another injury setback for Marquez.
"I'm not very worried," he insisted.
The Spaniard, who won six top-class titles in seven years from 2013, suffered a broken arm in the opening race of the 2020 season and did not race again that campaign.
He underwent a fourth surgery on his right arm in 2022 and has also suffered from double vision.
Reigning world champion Francesco Bagnaia of Ducati won Sunday's race.
