Brouwers' father was police commssioner in Hilversum and voted for the conservative liberal VVD. Brouwer studied Law at Groningen University. In law school Brouwer came into contact with the social security law and socially engaged lawyers. Inspired by this side of the legal profession, Brouwer became a member of the Communist Party of the Netherlands. In 1981 she became a member of the Tweede Kamer for the CPN. In 1981 she succeded Marcus Bakker as chair of the CPN parliamentary party. She would remain in the Tweede Kamer until 1986 when the CPN lost its three seats in the election and disappeared from the Tweede Kamer.
Brouwer was a long time proponent of a merger of the CPN, the progressive Christian Political Party of Radicals and Evangelical People's Party and the leftwing socialist Pacifist Socialist Party to form a new leftwing formation. In 1989 this happened in the form of the GreenLeft. After the 1989 elections Brouwer returned to the Tweede Kamer, as member of the GreenLeft. Between 1990 and 1991 she briefly left the Tweede Kamer in order to give birth. She was one of the first MPs to give birth during a term in parliament. Before the 1994 elections the GreenLeft held a referendum under its membership about the position of top candidate in the upcoming elections. Two duos entered the race. Ina Brouwer/Mohammed Rabbae, and Paul Rosenmöller/Leonie Sipkes. The Brouwer-Rabbae combination won the referendum, but lost the generale election. Against expections the party lost one of its six seats. Brouwer announced that she would not take her seat in parliament.
Between 1995 and 2003 Brouwer worked at the Ministry of Social Affairs and Employment as director for emancipation and quarter maker of the Academy of the ministry. In 2003 she published a book Het glazen plafond. Vrouwen aan de top, verlangens & obstakels ("The Glass ceiling. Women on top, desires and obstacles") on the position of women on the labour market. In 2005 Brouwer became senior advisor at Twynstra Mudde, where she advices public institutions on issues of diversity, social affairs and government reform.
In January 2007 Ina Brouwer announced that she became member of the Labour Party in addition to her membership of the GreenLeft. She did this in protest of the way the GreenLeft had operated during the cabinet formation where the GreenLeft decided not to participate further in the negotiations with the Labour Party the Christian Democratic Appeal, and the ChristianUnion. Brouwer thought that this was a missed opportunity.
When Prime Minister of the Netherlands Ruud Lubbers accidentially called her "Mrs Bakker" in parliament (a reference to her predecessor as fractievoorzitter of the Communist Party of the Netherlands, Marcus Bakker, Brouwer took offence. Lubbers send a box of chocolates to her, but Brouwer send them on to Mrs Marcus Bakker.nl:Ina Brouwer