The France international had seemingly been earmarked to start the campaign as the team's number one striker following an impressive pre-season, but he missed the opening two fixtures against Brighton & Hove Albion and Brentford due to a hamstring problem.
Martial played the second 45 minutes against Liverpool on August 22, providing the assist for Marcus Rashford to score, but he has been absent from the last three games against Southampton, Leicester City and Arsenal due to an Achilles problem.
Speaking during Wednesday's pre-match press conference, Ten Hag confirmed that the 26-year-old would again be missing for Thursday's European contest.
"Yes, he's [Martial] still out, he's progressing, but he's not ready to play," the Dutchman told reporters.
Martial also faces a battle to be available for Sunday's Premier League clash with Crystal Palace, when the Red Devils will be looking to put a fifth straight league victory on the board.
A recent report claimed that Cristiano Ronaldo is in line to start on Thursday, with the Portugal international building his fitness from the bench in recent games.
Ten Hag has said that the 37-year-old, who pushed for a move away from the 20-time English champions over the summer, is now "ready to start".
"He started against Brentford, then not since, but he is ready to start. Of course [he can start for the majority of games]," the Dutchman said when asked about the Portugal international.
Rashford thrived against Arsenal on Sunday, scoring twice in the 3-1 win over the Gunners, and he now has three goals and two assists in six league appearances this term.
The 24-year-old's struggles last term led to suggestions that he could be sold this summer, and there was allegedly interest from Paris Saint-Germain late in the transfer window.
However, Ten Hag has said that he is currently dealing with "a happy Marcus Rashford", with the Englishman "working really hard" since his time as head coach.
"Once again, it's difficult for me to talk about the past. What I see is a happy Marcus Rashford. We worked really hard the last two months with him on different aspects," Ten Hag told reporters.
"He likes it, he wants to transfer it to the pitch. It started with happiness, he comes in every day, he enjoys it, he's smiling, a really positive vibe, and if you put all of those things together - like the way of play - and you are happy, you will contribute more to the team."
As well as Ronaldo, Harry Maguire, Victor Lindelof, Luke Shaw, Fred, Casemiro and Anthony Elanga are also said to be pushing for starts against Real Sociedad.