Correspondents say the postponement is a sign of increased tensions between uneasy allies.
US-Pakistan relations reached a new low in November, when a Nato air attack killed 24 Pakistani soldiers.
Last week the US state department said that it had “received word” that Mr Grossman’s visit would be delayed.
A Pakistani official told Reuters that “Ambassador Grossman asked to visit Pakistan but we conveyed to him that it was not possible at the moment”.
Pakistan said in early December it had decided to review co-operation with the US and Nato. The review is currently before parliament with no fixed time for its recommendations to be presented to the government.
US State Department spokesman Mark Toner said on Tuesday Pakistan had decided the review should be completed before Mr Grossman’s next visit.