The Tokyo Olympics scheduled for later this year have been postponed until the next year. This in mind, did anything similar happen when the Spanish Flu was ongoing?
It actually saw the Stanley Cup final cancelled for the first time (the second would be in 2005 due to a labour stoppage; 2020 may also be cancelled, we'll see).
In 1919 there were two major professional hockey leagues: the NHL (National Hockey League; which had teams in Montreal, Ottawa, and Toronto), and the PCHA (Pacific Coast Hockey Association; teams in Vancouver, Victoria, and Seattle). Similar to baseball, the champions of each league would play each other in a series to determine who won the Stanley Cup, with the host alternating years (even was the NHL, odd was PCHA). In 1919 the Montreal Canadiens won the NHL title, while the Seattle Metropolitans won the PCHA, and Montreal went west to play Seattle.
The series was a best-of-five, meaning a team had to win three of the five games. As the leagues also had slightly different rules (the most notable being the PCHA had an extra player on the ice), games alternated between NHA and PCHA rules. Seattle won the first and third game, while Montreal won the second, while game four was tied 0-0, and 20 minutes of overtime failed to see any goals. With players exhausted, it was called off. There was discussion of how to play game five, and it was resolved they would play that game, and any future ones, until a winner was declared. Montreal won in overtime, tying the series at two wins, two losses, and a tie for each. This was on March 29, and a game six was scheduled for April 1.
However in the days before game six, several Montreal players took ill with the influenza going around. Five of them ended up in the hospital, and as the Canadiens only had 13 players on the roster, that was a considerable number. They waited to see if things would improve, but decided only five hours before game six to cancel the match. Montreal offered to forfeit the Stanley Cup as a result, but this was declined by Seattle, who didn't want to accept it under the circumstances. Montreal then asked if they could use players from the Victoria team (a not-uncommon practice of the era, when players would occasionally be loaned for a game or two; but never five at once), but the PCHA president refused this request. So on April 2 the series was cancelled, and for the fist time since the Stanley Cup was introduced in 1893, no winner was declared (as noted this would not happen again until 2005). Traditionally the winning team had it's name and those of the players engraved on the Cup, but for this series it simply says:
"1919 Montreal Canadiens
Seattle Metropolitans
Series Not Completed"
A further note: four of the Canadiens players recovered from the flue and continued their career. But one did not: "Bad" Joe Hall, a notorious tough player who had been highly regarded during his 17-year career. He was 37, old for a hockey player at the time, and his symptoms worsened, and on April 5 he died. He was the only hockey player to die of the influenza, though Canadiens manager George Kennedy would die in in 1921 of health complications related to it.