The midfielder was taken off in the 20th minute of Holland's 6-0 win over Latvia last Sunday with a knee injury.
Van Gaal said initial tests on the player's knee proved inconclusive and he will undergo another scan the week after next to determine how long he would be out for.
The United boss said: "He is not ready to play.
"He has a brace on his knee and 10 days' rest and then we have to make another scan and then we can say more about his injury.
"It is not so bad as the doctor thought after the match but it shall be a long story, I believe - but not six months or something like that.
Blind was one of five United players injured on international duty.
Luke Shaw felt a tight hamstring and groin while away with England and could miss Saturday's game at Arsenal.
"Shaw is a question mark," Van Gaal said.
Michael Carrick also suffered a groin problem on international duty, and he will be assessed before Van Gaal decides whether to include the player in the squad for the game at the Emirates.
"I have to wait for how he reacts (on Friday) and training sessions tomorrow but I expect that he is also ready to play," Van Gaal said.
There was better news about Angel di Maria and David de Gea, who suffered foot and finger injuries while away with Argentina and Spain respectively.
"Di Maria has trained today normally so I don't think that is a question mark (whether he is fit for Arsenal)," Van Gaal said.
"David De Gea is good, no problem."
The fact that Di Maria and De Gea look set to play against the Gunners is a big boost to Van Gaal.
The Dutchman's squad was already hit by injuries to key players before the international break.
Phil Jones, Marcos Rojo, Jonny Evans, Rafael and Radamel Falcao all missed the 1-0 win over Crystal Palace two weeks ago, and it looks like they will miss Saturday's game against the Gunners too.
When asked whether any player who missed the Palace match was available for this weekend, Van Gaal seemed to suggest it would be highly unlikely.
"It's difficult to say if anyone is back because we have to wait for tomorrow's training session to decide if players are coming back," he said.
"But the players are not coming back in the squad - that's a different thing
My philosophy is that you have to train at least one week with the squad, but better two."
Source : PA
Source: PA