MPs have given permission for Suffragette, which tracks the struggle for women to get the vote, to shoot on the estate over the Easter recess.
In the past no commercial filming has been allowed in the parliamentary buildings, with producers forced to assemble replicas of the historic chambers.
However, the Commons authorities have decided to carry out a pilot in a bid to raise revenue and cut running costs.
Streep - who won an Oscar for her portrayal of Margaret Thatcher in The Iron Lady - is reportedly playing feminist Emmeline Pankhurst in the film. British actors Carey Mulligan, Helena Bonham Carter and Ben Whishaw also have leading roles in the film.
Sir Alan Haselhurst, chairman of the cross-party administration committee, said: "Films will only be allowed if their subject matter is appropriate."