The officers stopped the man at a road block last week on the pretext of an arrest, investigators allege.
But after being taken to a police station, he was moved to a hotel, where payment was demanded for his release.
The man, whom the BBC is not naming, is believed to have been freed after the ransom was paid.
The British Embassy confirmed they were aware of the incident but they told news agency AFP the investigation was being handled by local police.
According to local media, the man was reported missing by his wife on 31 October.
He had been stopped on one of the city's highways and taken to the police station before ending up in the hotel in east Jakarta, where his alleged captors interrogated him all day.
It ended with them demanding he call his boss to ask for the ransom, to be paid in US dollars
But police swooped on the suspects as they attempted to convert the money into local currency.
Jakarta Police spokesman Argo Yuwono told CNN Philippines the kidnap attempt had involved "unscrupulous" members of the police force.
Two civilians are also under arrest for their alleged roles in the man's abduction.
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