The Canadian faces Thiem in the first singles match at 1pm on Friday, to be followed by World’s Jack Sock up against Europe’s Fabio Fognini.
Stefanos Tsitsipas (Europe) and Taylor Fritz (World) will open the evening session at 7pm, before Roger Federer teams up with Alexander Zverev in doubles for Europe against Shapovalov and Sock for World.
With one point available for each match on Day 1, Captains John McEnroe (World) and Bjorn Borg (Europe) will hope to make early progress towards the required 13 points that will claim the Laver Cup.
Team World did not manage to win an opening-day singles match in the first two Laver Cup instalments in 2017 and 2018, and ultimately went on to lose out to Team Europe.
Shapovalov will hope to turn that around and get the red team off to a winning start on Friday, but he faces a formidable opponent in world No.5 Thiem.
Fognini looks a strong favorite over Sock in terms of rankings (11-210) but the pair share a 1-1 record from previous matches, while the evening session begins with a first meeting between rising stars Tsitsipas and Fritz.
Team World has impressed in doubles in the past and Sock and Shapovalov will need to be at their best up against home hero Federer and Zverev – plus a healthy section of the 17,000 fans at Palexpo.