"(Marquez) suffered a ... fracture to his right humerus," Honda said in a statement, adding that he would travel to Barcelona for surgery.
"MotoGP medical staff have confirmed there is no other serious head or thoracic trauma but (he) will remain under observation for 12 hours."
Petronas Yamaha's Fabio Quartararo took his first MotoGP victory on Sunday, winning an incident-packed Spanish Grand Prix in Jerez
Quartararo's victory was also the first for Petronas Yamaha as he finished ahead of Yamaha's Maverick Vinales and Ducati's Andrea Dovizioso, who came third just weeks after having surgery on a damaged left collarbone.
"It felt amazing but strange to realise it because you (usually) have the fans around the track," Quartararo told reporters.
"We need to enjoy today a lot because it's not everyday that you have your first MotoGP victory and from tomorrow we will focus on next week's race."
From his pole position, Frenchman Quartararo had a poor start and dropped to fourth in the first lap as Vinales took the lead, with Pramac Ducati's Jack Miller also looking for a podium finish.
There was drama at turn four when Marquez lost control of his bike and went into the gravel, but the defending world champion managed to rejoin the race in 18th place.
Vinales, who had started with a soft front tyre, was struggling with 17 laps to go and went wide, dropping to third, while Quartararo took advantage to move back into the lead with Miller in second.
Further back Marquez began to carve his way through the pack and eventually moved up to third with five laps left.
But as Marquez challenged Vinales for second, he was catapulted off his bike at turn four before bouncing off the track and into the gravel.
Marquez walked away from the crash with the help of track marshals but was clearly in pain after being hit by the bike and was later put in a neck brace before being taken to a medical centre.
"Marc took a big hit to the upper arm, now they are checking it and doing an X-Ray," Honda team manager Alberto Puig said.
Miller finished fourth while Franco Morbidelli gave Petronas Yamaha another reason to cheer when he came fifth.