The suspect was detained during Friday's first ODI of the controversial tour, held despite the country's deadliest terror attack on a Dhaka cafe in July.
All-round Mortaza inspires Bangladesh
"Our anti-corruption officials found his movements suspicious, so they detained him and handed him over to local police," said Bangladesh Cricket Board (BCB) spokesman Jalal Yunus.
Gambling is illegal in Bangladesh, whose cricket authorities threw out four Indian nationals last year for suspected involvement during a T20 tournament.
Local police official Bhuiyan Mahboob Hossain said the suspect had been handed to the Indian High Commission after being interrogated, and had not been charged.
England beat Bangladesh by 21 runs in first ODI
England agreed to tour Bangladesh only after the Bangladeshi authorities promised "unprecedented" security during the month-long tour.
The three-match ODI series is currently locked at 1-1 after England won the first match by 21 runs and Bangladesh levelled with a 34-run win in the second match.
The two teams will head now to Chittagong, where the third and final match of the series will be held on Wednesday. The teams will also play two Tests.
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