Former world number one Murray returned after almost a year out with a hip injury at this week's Queen's Club tournament, but lost in the opening round to Nick Kyrgios.
With Wimbledon looming Murray, twice a champion at the grasscourt Grand Slam, took an Eastbourne wildcard on Friday in a bid to test his fitness for the All England Club fortnight.
After losing to Kyrgios in three sets the 31-year-old expressed some doubt over his ability to play best-of-five-set matches and said he could even miss the tournament he won in 2013 and 2016.
While Murray has slid to 156th in the rankings, Wawrinka has dropped to 261st, having played only a handful of matches this year following left knee surgery in 2017.
Both would have wished to avoid such a demanding first round clash on the south coast, where Wawrinka also took a wildcard in a bid to regain match sharpness for Wimbledon.
The winner of their match will play second seed Kyle Edmund, who has taken over from Murray as Britain's number one.
(Reporting by Martyn Herman; Editing by Andrew Bolton)
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