The factory Ducati rider and his Gresini counterpart on a year-old Desmosedici were battling over fifth in the closing stages of Sunday’s 25-lap grand prix in Portugal.
Marquez launched his GP23 up the inside of Bagnaia on lap 23 but ran slightly wide having moved ahead of the factory Ducati.
As he cut back to try to defend the position, Bagnaia came back up the inside and the pair collided.
Both riders crashed as a result of the contact, with Marquez remounting to finish 16th while Bagnaia retired in the pits moments after the tangle.
The collision was placed under review by the MotoGP Stewards Panel, but it was deemed a racing incident and no punishment was apportioned.
A brief note from the FIM read: “After hearing with both riders and further review, [it] was determined to a be a racing incident. No further action.”
The collision marks the first test for Ducati in how it manages its roster since Marquez signed for Gresini.
What will make Ducati’s situation trickier is the fact Marquez is not directly contracted to the manufacturer.
Bagnaia is now 23 points behind Portugal GP winner and Pramac Ducati rival Jorge Martin, having thrown away a likely sprint win on Saturday with an error late on.
Marquez is now 27 points off the championship lead, with his first podium on the Ducati in the sprint on Saturday softening the blow to his position in the standings.
Both riders are yet to speak to the media.
The collision between the pair provided a boost to the factory KTM squad. Its riders Brad Binder and Jack Miller moved up to the top five, having been quickly dropped in the early stages of the race.
Just moments before the incident, Tech3 rookie sensation Pedro Acosta had overtaken Bagnaia for fourth, having dispatched Marquez on lap eight.
Acosta went on to finish on the podium for the first time after Aprilia’s Maverick Vinales suffered a suspected gearbox issue and crashed on the final lap.