"I do not work on Mondays."
Translation:Eu não trabalho às segundas-feiras.
A good way to check for yourself whether a particular collocation works is by using the site http://www.linguee.com/portuguese-english. If I enter "nas segundas-feiras" I get a number of hits which seem to be translated as "on Mondays" so that leads me to believe it is valid. Of course, you can't beat getting advice from a native speaker, but this is the next best thing.
They ask for the preposition A when they indicate an action that is repeated:
Meu plantão é às quintas-feiras (every Thursday).
My duty is on Thursdays. Os museus fecham às segundas-feiras (every Monday). Museums close on Mondays
The preposition EM (no sábado, na segunda) gives the following message: the fact will occur only once or from time to time. No regular repetitions:
Vi Maria no domingo.
I saw Maria on Sunday.
O filho deles nasceu na quarta-feira. Their son was born on Wednesday.