Wales' main exam body, the WJEC, decided last year to stop offering the course in either English or Welsh due to a low uptake.
Regulating body Qualifications Wales invited exam boards from England to provide the course but did not insist it was available in Welsh.
The teacher behind the petition called it "linguistic discrimination".
Chris Evans, who established a psychology department at Ysgol Morgan Llwyd in Wrexham, wants the Welsh Government and Qualifications Wales to "change the policy".
Another exam board, Pearson, is offering psychology through the medium of English for students in Wales from September 2017 but would not provide it in Welsh, partly because it did not have "access to the expertise".
It means psychology is one of a number of GCSE subjects, including economics, available in English in Wales but not in Welsh next year.
A Qualifications Wales spokesperson said it was in discussion with two exam boards about putting Welsh-medium provision in place next year.
"As part of the reforms of GCSEs, GCSE Psychology was one of the subjects for which the potential number of candidates in Wales was too low for a qualification designed specifically for Wales to be viable," they said.
"A new A level Psychology for Wales was introduced in 2015 by WJEC and is available bilingually.
"As we have done for other low-take-up subjects, we have designated for funding in Wales three GCSE Psychology qualifications that have been designed for England. These are not currently offered through the medium of Welsh.
"We know there is a demand for GCSEs in this subject to be available in Welsh and we are still looking at how that could be achieved.
"We are in discussions with two exam boards, WJEC and Pearson, to see if there is a way of putting arrangements in place to secure Welsh-medium availability for next year."
A petition has been launched against a decision by an exam board to stop offering psychology GCSE next year.