Both players were injured during the 2-1 defeat to Crystal Palace last Saturday and will be unavailable for Saturday's 12:30 BST kick-off at St Mary's.
In-form attacker Martial scored twice during his first-ever away appearance as a United player, at the south-coast ground back in 2015.
Left-back Shaw, who has a hamstring problem, will miss out on a reunion with his former club.
Manager Ole Gunnar Solskjaer should provide an update on the situation ahead of the clash against the Saints in his pre-match press conference, which will be held at the Aon Training Complex on Friday morning.