Craigcefnparc Primary School and Ysgol Gynradd Gymraeg Felindre have been chosen on the grounds of declining pupil numbers.
Gower MP Tonia Antoniazzi said the village of Craigcefnparc was “on the verge of having its heart ripped out”.
The ruling Labour cabinet also approved plans to build two new Welsh-medium schools in Clase and Penlan.
Ms Antoniazzi urged the cabinet to give Craigcefnparc Primary School, which has 49 pupils, more time to make improvements and increase pupil numbers, according to the Local Democracy Reporting Service.
“It is, I believe, within the gift of this authority to make this work,” the Labour MP told the cabinet meeting on Thursday.
Jennifer Raynor, cabinet member for education, said the school had falling numbers and had already been offered four years of “intensive support”.
She said youngsters would be better off at Clydach Primary School, where they would go from next September.
Councillor Raynor added that numbers at Ysgol Gynradd Gymraeg Felindre, which has just 14 pupils, were also “in a long-term decline”.
Conservative group leader Lyndon Jones claimed “big is not always better” when it came to schools.
“Craigcefnparc primary has been in difficult times, but it is starting to thrive,” he told the meeting.
Conservative councillor Brigitte Rowlands, whose Mawr ward includes both schools, said she and local campaigners would seek legal advice, warning: “We are not going to accept this decision.”
Suzy Davies, Conservative education spokesperson in the Welsh Assembly, has said she will raise the Craigcefnparc closure with the children’s commissioner for Wales.
The closures need to be confirmed at a Swansea Council cabinet meeting in March once any objections to the statutory notices have been considered.