The 35-year-old had been due to play Taro Daniel, who knocked him out of this year's Australian Open, in qualifying on Saturday evening, but has now taken the unused special exempt spot, which opened up following fellow Brit's Jack Draper’s defeat in Montreal on Friday.
Murray is a previous champion in Ohio, having won the Masters Series event in 2008 and 2011. He also made the final in 2016.
Being promoted into the first round is a boost for Murray, who would have faced a tough encounter against Daniel. He lost in the first round of the Rogers Cup to Taylor Fritz earlier this week and has found it hard to rediscover his grass-court form of earlier in the summer.
Should Murray defeat Wawrinka, then he is likely to play British No 1 and ninth seed Cameron Norrie in the second round, should he defeat Holger Rune of Denmark.
Meanwhile, the soon-to-retire Serena Williams has emerged as Emma Raducanu’s next challenge as the Briton prepares to defend her US Open title.
The world number 10 has been drawn to face Williams in the first round of the Western and Southern Open, which begins with qualifying this weekend and is likely to be the American’s final tournament before the US Open.
The 23-time grand-slam champion this week indicated she would retire after contesting Flushing Meadows, saying she was “evolving away from tennis, toward other things that are important to me”.
“As I said in the article, I’m terrible at goodbyes. But, goodbye Toronto,” a tearful Williams told the National Bank Open crowd after losing in straight sets to Belinda Bencic in the second round.
Raducanu, 19, went home a round earlier in Toronto, with her 7-6 (0) 6-2 defeat to defending champion Camila Giorgi following a quarter-final loss to Liudmila Samsonova at Washington’s Citi Open.
Monday’s match is the first meeting between Raducanu and Williams and comes 23 years since the latter won the US Open for the first time, also as a teenager.
The winner of the first-round encounter will next face either Victoria Azarenka or Kaia Kanepi.