Scarlets prop Alex Hepburn has also been called up.
In Sunday's bruising encounter with South Africa, lock Williamson suffered a hand injury after coming on as an early replacement following Scott Cummings' red card, while flanker Brown, who did not feature at Murrayfield, has a rib injury.
Hooker Matthews, who has one Scotland cap, was a surprise absentee from Gregor Townsend's original squad following fine form for his club.
Fellow 31-year-old Hepburn has four caps.
Portugal visit Murrayfield on Saturday before Australia conclude Scotland's Autumn internationals on 24 November.