Martial missed United's season-opening defeat by Brighton & Hove Albion and the heavy loss to Brentford before coming on as a substitute against Liverpool on Monday, where he provided an assist to Marcus Rashford in their morale-boosting 2-1 win.
"Martial is not fit. He came out with a problem on his Achilles, so we have to wait," Ten Hag told reporters ahead of Saturday's match at St Mary's Stadium.
"I cannot tell a prognosis on how long it takes but we hope he'll be available for the next game against Leicester City."
United's new signing Casemiro (30) watched from the Old Trafford stands as United overcame Liverpool and the former Real Madrid midfielder could make his debut for the club at Southampton.
"Casemiro is fit. He did all of the training sessions. He trained first individually and in the last days, he trained with the team," Ten Hag added.
"The spirit was already good but now it's even better (after Monday's victory). But it's only one game, so we have to build further, we have to develop and everyone is aware of that.
"We need to have a high standard. It's a demand to the group. Now they see what the reward is, so we have to match the runs in and out of possession. We need runs and movement if you want to dictate a game."
United have been linked by the British media with a move for Ajax forward Antony (22) before the transfer window closes on September 1st.
"We need players but we need the right players," Ten Hag added. "The whole transfer window, we are happy with what we did until now, but the bar has to be high."
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