Veltman was unable to finish his side's 2-0 win over Bundesliga outfit Schalke in Doha on Saturday, due to a mild strain of his left hamstring.
With Frank de Boer's side set to return to their domestic campaign on Friday against Groningen, the Ajax boss confirmed Veltman was likely to miss the game.
"I'm not expecting that he'll be able to play on Friday against Groningen," said de Boer.
"That's a bitter pill for him and for the team. But Mike van der Hoorn has shown that he's ready, too."
Ajax trail Eredivisie leaders PSV by four points midway through the campaign, with De Boer's men winning their last three league games prior to the mid-season break.
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