Bardsley had only just returned to the international setup after being overlooked by Gordon Strachan for eight months, but the Stoke City full-back suffered a groin strain against Tottenham on Sunday.
The 29-year-old was forced off in the ninth minute at White Hart Lane and had to watch on as his team sealed a 2-1 victory thanks to goals from Bojan and Jonathan Walters.
Former Sunderland man Bardsley will not feature in Friday's Euro 2016 qualifier against Ireland at Parkhead or the friendly against England at the same venue next Tuesday, so Paterson could make his international debut.
The London-born 20-year-old has scored one goal in six league appearances for Hearts this season, as Robbie Neilson's side have charged to the top of the Championship with 10 wins from their 12 matches.
He is the second player to be added to Strachan's squad in as many days after Johnny Russell was called up in place of injury Derby County team-mate Craig Bryson.
