Pole sitter Marquez lost position in the opening laps of the Portuguese Grand Prix on Sunday to drop to fourth when he clipped Pramac Racing's Jorge Martin before barging into RNF Racing's Oliveira who was in second place.
Marquez and Oliveira crashed out of the race after the incident. Marquez, a six-times premier class champion, later apologised for his mistake.
"Upon returning to Spain for further checks, Marc Marquez was diagnosed with a displaced intra-articular fracture of the base of the first metacarpal of the thumb of the right hand," Honda said in a statement.
"After surgery to repair the broken first metacarpal in his right hand, Marc Marquez will miss the second round of the 2023 MotoGP World Championship."
The Argentina GP will be held this weekend at the Termas de Rio Hondo Circuit.