The world number two pulled out of the ATP Cup last week with the niggle and said ahead of the Australian Open that he was "suffering".
Australian Open 2021, men's preview: Can anyone end Novak Djokovic's 'love affair' with Melbourne Park?
Novak Djokovic has won eight times at Melbourne Park in 16 visits going back to his first-ever major in 2008. In the last 10 years, he's won seven times.
Medvedev needed to dig deep against Alexander Zverev, finally coming through 3-6, 6-3, 7-5 on his fourth match point
Rafael Nadal was once again missing from the Spanish team as they lost 2-1 to Greece.
Zverev had to dig deep for his 6-7 (5/7), 6-3, 7-6 (7/4) win to seal the tie, but gained valuable court time ahead of another crack at a first Grand Slam trophy at the Australian Open starting next week.
The 20-time Grand Slam champion was due to take the court against Australia's top-ranked player Alex De Minaur, but opted to rest instead as he prepares for the Australian Open next week.
ATP Cup 2021: Novak Djokovic makes perfect start with win over Denis Shapovalov; Dominic Thiem suffers defeat
Djokovic showed no signs of being hindered by a nasty blister on his racquet hand that troubled him at an Adelaide exhibition last week and returned 30 minutes later alongside Filip Frajinovic to play the decisive doubles rubber.
Slimmed down ATP Cup 2021 gets underway on Tuesday with smaller field of 12 nations and a lighter prize cheque.
Dominic Thiem's father is the captain of the Austria ATP Cup team, where his son opens his season with a tough match against Italian world number 10 Matteo Berrettini
Former top-five star Nishikori was among 72 players forced to stay in their rooms 24 hours a day after COVID-19 cases were detected on charter flights bringing them to Melbourne for the Australian Open.
Australian Open 2021: Rafael Nadal says he is ready to perform for 'suffering' fans around the world
Rafael Nadal kicks off his season representing Spain at the ATP Cup from Tuesday.
Serbians faced a tricky draw in Group A against the Alexander Zverev-inspired Germany and a Canada team featuring Denis Shapovalov and Milos Raonic.
The charters and the early arrivals are all part of Tennis Australia's attempt to have the tournament happen despite a ban on international arrivals into the country.
Thiem's father told Austrian media that he would train with Dominic and fellow Austrian Dennis Novak.
Each tie will be comprised of two singles matches and one doubles. The draw will be made on 20 January ahead of the tournament starting on 1 February.