Veltman sustained the blow in Ajax's 2-0 friendly win over Schalke last Saturday.
No timeframe has been set for for Veltman's return, although the Dutch champions confirmed that he would be on the sidelines for "a few weeks."
In 21 appearances in all competitions this season, Veltman has found the net three times for an Ajax side that sits second in the Dutch top flight, four points behind PSV.
Veltman broke into the Netherlands national team in November 2013 and made two appearances at the World Cup.
Ajax host Groningen at the Amsterdam Arena on Friday as they restart their bid for a fifth consecutive Eredivisie crown.
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