The Cardinals recalled outfielder Conner Capel and catcher Iván Herrera and selected infielder Cory Spangenberg from Triple-A Memphis as substitute players for their two-game series north of the border.
Foreign nationals who aren't vaccinated against COVID-19 are not allowed to enter Canada, save for limited exceptions that require a 14-day quarantine. Unvaccinated baseball players are placed on the restricted list, where they are not paid and do not accrue major league service time.
Arenado will lose $384,416, Goldschmidt $241,758 and Romine $10,989.
A seven-time All-Star and four-time Gold Glove Award winner, Goldschmidt leads the Cardinals in most offensive categories, including batting average (.333), home runs (22), RBIs (74), on-base percentage (.416) and hits (116).
Goldschmidt, who homered during last week's All-Star Game in Los Angeles, connected twice during Sunday's 6-3 loss at Cincinnati, extending his homer streak to four games. St. Louis was off Monday.
Arenado is a seven-time All-Star and a nine-time Gold Glove winner who has led the National League in home runs three times. Arenado has 102 hits, 18 home runs and 59 RBIs this season.
Romine joined the Cardinals earlier this season as backup for the injured Yadier Molina (right knee), who is expected to rejoin the team next month.
Right-hander Johan Oviedo, who is from Cuba, was able to join the Cardinals in Toronto despite having an expired passport. Oviedo flew to Miami on Monday's off day to collect travel documents from the Canadian consulate there. He then flew to Detroit and drove the 230 miles to Toronto, arriving late Monday.