The full-back was forced off on a stretcher in the 70th minute of the Gunners' 2-0 win on Saturday after falling awkwardly when challenging for the ball.
And the club have now confirmed that he faces between six and nine months on the sidelines, meaning he could also be ruled out of the start of the 2019-20 campaign.
"Further to the injury sustained during our match against Chelsea on Saturday, we can confirm that Hector has ruptured the anterior cruciate ligament of his left knee," a statement read.
"Hector will undergo surgery to repair this in the coming days. The rehabilitation process is expected to take between six to nine months and therefore rules Hector out of action for the remainder of this season.
"Everyone at the club will now be working as hard as we can to ensure Hector is back on the pitch as soon as possible next season."
Spain international Bellerin had only just returned to the Arsenal side having missed the festive run of fixtures with a calf strain.
And Unai Emery will now have to again do without his first choice right-back as he looks to end his first season in charge in a positive manner.
Stephan Lichtsteiner is the most obvious choice to provide cover for Bellerin during the second half of the season, though Ainsley Maitland-Niles has been used as a right wing-back in recent weeks when Emery has utilised a three-man defence.
Carl Jenkinson, meanwhile, remains part of the squad at the Emirates Stadium and could be afforded some minutes should he be required to deputise.