Jindal told Fox News, "This is not my time."
He said he's not ready to endorse another candidate, but intends to support the eventual Republican presidential nominee.
The governor, who is term-limited and will be out of office in January, said he will work with a think tank he started a few years ago, called America Next.
Jindal focused his entire campaign effort on the early voting state of Iowa. But he never won much support there against higher-profile Republican contenders Donald Trump and Ben Carson. Jindal's fundraising lagged, and his low poll numbers kept him off the main debate stages.
Jindal, 44, was the first person of Indian-American heritage to run for U.S. president. A Christian who converted from Hinduism as a teenager, his message was aimed at social conservatives and evangelical Christians.
Former Iowa Republican Party Chairman Matt Strawn said Jindal's withdrawal would buoy U.S. Senator Ted Cruz of Texas, who appeals to the same evangelical voters and on Monday won the backing of an influential Iowa lawmaker.
"It means a good week for Senator Cruz just got better as he attempts to consolidate evangelical and anti-establishment support in Iowa," Strawn said.
Louisiana voters will go to the polls on Saturday to pick Jindal's successor as governor.
Wire services
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