A magistrate in the capital Dhaka delivered the order after 19-year-old Naznin Akter Happy lodged a complaint of "rape" and a "false promise of marriage" against the cricketer last month.
The court's decision puts a huge question mark over the 24-year-old's appearance in the next month's World Cup in Australia and New Zealand after selectors picked him in the 15-man squad last weekend.
"The metropolitan magistrate court rejected his bail plea... He was sent to prison pending the next hearing of the case," deputy commissioner of Dhaka police Anisur Rahman told AFP.
Police last month launched a probe after Happy lodged a complaint with police that the fast bowler had backed away from an earlier pledge to marry her after having a months-long "intimate affair".
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After hearing the complaint, a court ordered medical tests on Happy and both the alleged victim and Hossain to undergo DNA tests.
The scandal has gripped the conservative Muslim-majority country for weeks, with Happy telling reporters that she would be prepared to withdraw the case if Rubel agrees to marry her.
Although victims of alleged rapes are usually entitled to anonymity, Happy's decision to go public prompted police to waive the usual restrictions. Under Bangladeshi law, anyone who makes what is considered a "false" marriage proposal is liable to criminal prosecution.
Happy became a household name for her debut movie "Kichu Asha Bhalobasa" (Some Hopes, Some Loves) which hit the cinemas in September 2013.
After filing the complaint, Happy told private Channel-71 that they "had a relationship like any other couple" but that "recently, he was finding excuses not to marry me".
"It's an act of cheating and I want him to be punished," she said without elaborating on the rape allegation.
Rubel has played 22 Tests for Bangladesh and taken 32 wickets. He has also taken 69 wickets in 53 one-day international matches including a hat-trick against New Zealand.