Mwesigwa is both a given name and a surname. Notable people with the name include:
Mwesigwa Rukutana, Ugandan lawyer Alice Mwesigwa (born 1969), Ugandan teacher and lecturer Andrew Mwesigwa (born 1984), Ugandan footballer Elizabeth Mwesigwa (born 1992), Ugandan badminton player Isaac Mwesigwa, Ugandan businessman Robert Mwesigwa, Ugandan politician Sheldon Mwesigwa (born 1962), Ugandan bishop