Honda said in a statement that the 22-year-old's participation in his home Spanish Grand Prix in Jerez next week had not been ruled out.
Marquez is fifth in the championship with 36 points after three races, with Yamaha's Valentino Rossi leading on 66 points thanks to two victories.
Honda said the rider, who broke his leg in a crash before the start of last season while training on a dirt track bike, went to hospital in Barcelona on Saturday morning and a subsequent X-ray showed the fracture.
"We decided to treat the injury, as we would in the case of any other patient, by fixing a titanium plate to his finger," said doctor Xavier Mir.
"This will allow us to initiate functional recovery after 24 hours and give him a chance of racing at Jerez."
Marquez's Repsol Honda team already have Spaniard Dani Pedrosa out of action after surgery to fix an arm problem, with Japanese rider Hiroshi Aoyama standing in for him.
(Reporting by Alan Baldwin, editing by Tony Jimenez)
