Unadkat is waiting for his visa to be processed in Rajkot.
He is expected to join the Test team in Chattogram over the next few days.
At the BCCI’s National Cricket Academy in Bengaluru, Shami is recuperating from a shoulder injury.
During a workout prior to the Bangladesh tour, he felt a pain in his right shoulder. Shami had a slim chance of being fit for the Tests after missing the ODI portion of the tour, but that has now been ruled out.
This is only the second time Unadkat, 31, has been called up to the Test squad. As a teenager just out of the India Under-19s.
He made his first appearance in the format almost exactly 12 years ago, in the first Test of the tour of South Africa from 2010 to 2011.
He finished that Test in Centurion with figures of none for 101, and India lost by 25 runs in an innings.
As an injury replacement, Unadkat is the second player who is likely to join India’s Test squad in Bangladesh.
A Bengal player who led India A to a 1-0 victory over Bangladesh A in the four-day shadow tour series, was called up on Friday evening to play in place of Rohit Sharma.
He has flown home to Mumbai to treat a finger injury he sustained in the ODI series.
Unadkat has led Saurashtra, the team he led to a flurry of domestic success in India, to an impressive body of work over the past five years.
He took a record-breaking 67 wickets, the most by a bowler in a season, during their first Ranji Trophy title win in 2019-20.
Unadkat has taken 115 wickets in 21 matches over the past three Ranji seasons.
Since the beginning of January 2019, Unadkat’s bowling average of 16.03 ranks among the highest in all of first-class cricket.
In these 24 matches, he has taken 126 wickets, including nine five-fors and three 10-wicket hauls, with a best of 7 for 56.
Unadkat said in an interview with ESPNcricinfo last week prior to the Vijay Hazare Trophy final.
Unadkat took the most wickets in the tournament, taking 19 in ten games, as Saurashtra won the tournament.
He had stated, “I do look at my individual performances, but from a perspective that takes the team through, not from a perspective of whether it will help me get selected for India or India A.”
Unadkat has developed his USP over time by bowling on Rajkot’s well-known lifeless decks.
He has taken a lot of wickets thanks to his ability to swing the new ball and reverse the old ball.
And his improved fitness has helped him play for longer periods, which he did tirelessly during the “career-defining” 2019-20 season.
Unadkat has also played in seven one-day internationals and ten one-day internationals.
He was last important for the India group during their Nidahas Prize mission in Sri Lanka in Walk 2019.