Which sports stadium had the world's first retractable roof?

The Skydome in Toronto.
http://www.projectballpark.org/major/skydome.html

Montreal's Olympic Stadium in 1988 was in use before the Skydome.
Problems plagued the stadium from the time it opened for the Olympic Games--which at that point was only half built. Seating 58,500 at the time, the stadium was not fully completed in time for the games due to strikes by construction workers, leaving it without a tower or roof for the opening and several years following. Both the tower and the roof, made of over 60,000 feet (approximately 18,500 meters) of kevlar, were not completed for over a decade, and it was not until 1988 that it was possible to retract the roof.
https://en.wikipedia.org/wiki/Olympic_Stadium_%28Montreal%29

While it wasn't precisely a "roof," the Roman Colosseum did have a canvas canopy that could be used to provide shade or protection from the elements.

Scroll down to "Description":
https://en.wikipedia.org/wiki/Colosseum

Rogers Centre, formerly known as (and often still unofficially called) SkyDome, [1] is a multi-purpose stadium in Toronto, Ontario, situated next to the CN Tower near the shores of Lake Ontario. It is home to Major League Baseball's Toronto Blue Jays and the Canadian Football League's Toronto Argonauts. While it is primarily a sports venue, Rogers Centre also hosts other large-scale events such as conventions, trade fairs, and concerts.
Rogers Centre is also noted for being the first stadium to have a fully retractable motorized roof, as well as a hotel attached to it, with 70 rooms overlooking the field.
https://en.wikipedia.org/wiki/Rogers_Centre

Pittsburgh Civic Arena, 1961

Actually, the first retractable roof stadium was Mellon Arena, which opened as the Pittsburgh Civic Arena in 1961 and is informally known as The Igloo. Although it was not originally designed for sports--the Pittsburgh Civic Light Opera was the primary tenant from 1961 until 1968--its been the home of the NHL's Penguins since 1967. The Light Opera moved out of the building because the acoustics, when opened, were not very good.

Mellon Arena predates other retractable-roof facilities, including Olympic Stadium in Montreal, Rod Laver Arena in Melbourne and Rogers Centre in Toronto by many years.

Wiki agrees:

The first retractable roof sports venue was the now-demolished Civic Arena in Pittsburgh, Pennsylvania, United States. Constructed in 1961 for the Pittsburgh Civic Light Opera, the arena was home to minor-league and NCAA D-1 basketball and ice hockey teams before becoming the home of the NHL's Pittsburgh Penguins in 1967, as well as hosting over a dozen regular season NBA games in the 1960s and 1970s.

https://en.m.wikipedia.org/wiki/Retractable_roof#The_first_stadium_retractables