"Today is #ZeroDiscriminationDay. As a proud Tunisian, Arab and African woman I celebrate the right of everyone to live with dignity," Jabeur tweeted.
She also shared a picture of a Tunisian stamp from 1961, celebrating "Africa Day".
Saied last week accused sub-Saharan African migrants of bringing a wave of "violence and crime" to the North African country and representing a "criminal plot" to change its demographic make-up.
Rights groups have criticized his comments as "racist" and accuse him of sparking violence against migrants.
Hundreds of West Africans, evicted in recent days by landlords fearing heavy fines for hosting undocumented migrants, have flocked to their embassies in Tunis to seek repatriation.
Another Tunisian sports figure, Radhi Jaidi, who comes from the black community that makes up around a tenth of the country's 12 million population, also voiced solidarity with migrants over the weekend.
"I'm African, not just because I was born in Africa, but because Africa was born in me," he said in an online post.
According to figures from the Tunisian Forum for Economic and Social Rights (FTDES), around 21,000 irregular migrants from other parts of Africa live in Tunisia.
That figure includes foreign university students and workers who complain they are unable to obtain the paperwork they need because of Tunisia's archaic bureaucracy.