According to the group, the thief smashed the passenger window of their tour van, as they took cover inside.
He mainly targeted electronics, including film cameras and laptops they use on stage.
They also lost all of their passports and documents, as well as suitcases containing their clothes, "so we're going to wearing the same things for the next two weeks".
Greenwood also lost her journal in the incident.
"I know it sounds ridiculous," she said, "but that's almost the worst part".
Luckily, the group's instruments were housed in a separate, locked compartment at the back of the van.
The band, who are promoting their forthcoming third album, Boys These Days, remain hopeful they can play the opening show of their tour on Tuesday night.
'We're definitely not going to let this put us off," said Greenwood.
"And ultimately, it really makes you reflect on things to be grateful for, both here and at home."
The tour will even return to the Bay Area on Saturday night.
"We're gonna keep playing," said Rice. "We've got nothing against the Bay Area. We think it's great here - but it's sad that it's kind of got to this sort of place with gun violence."