Serb second seed Djokovic was 6-4, 6-1, 3-1 ahead when Wawrinka, who had already complained of feeling unwell at the end of the third game of the third set, called it quits.
Djokovic, who was leading 2-0 overnight when the match was halted because of rain, goes on to face either 2009 champion Juan Martin Del Potro, the Argentine seventh seed, or 2003 winner Andy Roddick for a place in the semi-finals.
"It was a difficult situation for both of us with the rain yesterday. We were here for 10 or 11 hours, warmed-up and then stopped. It was hard to get
ready for a match that way," said Djokovic, the 25-year-old Australian Open champion.
Djokovic has reached his sixth successive US Open quarter-final by dropping just 20 games in four rounds.
"I'm happy with my performances. I played well against a quality opponent and I wish him a quick recovery," added the Serb, who played his match in front of just a few hundred fans on the 10,000-capacity Louis Armstrong Stadium.
Wawrinka, who was bidding to reach the quarter-finals for the second time, having made the last eight in 2010, has now lost 19 matches in a row against top-10 players.