The team said they would give the Canadian, son of the team's billionaire owner Lawrence, every chance to race.
"Should he not be fit to compete, then Felipe will drive the AMR23 alongside Fernando (Alonso)," they added.
Stroll missed the three-day pre-season test from Thursday to Saturday at Bahrain's Sakhir circuit with reserve driver Drugovich doing 117 laps as a stand-in alongside double world champion Alonso.
The team have given few details about Stroll's cycle accident during training in Spain, other than saying he had a wrist injury.
Aston Martin have two official reserves, the other being Belgian Stoffel Vandoorne (30) - a former McLaren F1 driver who is also the reigning Formula E champion and was racing in the electric series in Cape Town on Saturday.
The team's confirmation that reigning Formula Two champion Drugovich would race if Stroll cannot also addressed speculation that four-times world champion Sebastian Vettel (35) could make a surprise comeback.
Vettel retired at the end of last season but team principal Mike Krack told reporters in Bahrain they remained in contact and would not say whether the German was interested in returning.
Aston Martin started last season with a stand-in driver for the first two races in Bahrain and Saudi Arabia after Vettel tested positive for COVID-19.
Nico Hulkenberg (35) was the replacement that time but the German has now secured a full-time drive at Haas.
