Dupasquier's team, Prustel GP, did not take part in Sunday's race, while his fellow Swiss rider Tom Luthi pulled out of the Moto2 contest.
Dupasquier was in his second season in MotoGP's lightweight class and was in the top 10 in the overall standings heading into the weekend.
The MotoGP grid staged a one-minute silence ahead of Sunday's 23-lap race, which was won by world championship leader Fabio Quartararo.
Following his victory, the French rider stopped at the scene of Dupasquier's accident before pointing to the sky. He then waved a Swiss flag on the podium in Dupasquier's honour.
"It was tough because when you do the one-minute silence, the emotion is coming really quick and it is difficult to stay focused," said the 22-year-old Quartararo. "We got the win and that one was for Jason and his family."
Tributes flooded in from other riders, as well as from across the world of motorsport.
Formula One tweeted: "No words can ever describe the pain of such a loss. Our thoughts are with Jason's family, friends and the entire MotoGP community."
Many F1 teams and drivers also took to social media to express their condolences.
Ferrari's Charles Leclerc, who secured pole position at last weekend's Monaco Grand Prix, tweeted: "Rest in peace, Jason."