The 34-year-old Dhoni suffered the condition during the team's training session here.
"India ODI and T20I captain MS Dhoni has suffered a muscle spasm in the back during a training session today in Dhaka," BCCI secretary Anurag Thakur said in a statement.
"The All-India Senior Selection Committee has named Parthiv Patel as the back-up wicketkeeper for the upcoming Asia Cup, 2016. He will join the team in Dhaka at the earliest."
The 30-year-old left-handed wicketkeeper-batsman, Patel plays for Gujarat in the domestic circuit, and has had a good season at home, hitting a century each in Vijay Hazare and Deodhar Trophy tournaments.
Patel, who last played for India in an ODI against Sri Lanka in the tri-series at Brisbane, Australia in 2012, had recently expressed a desire to return to the national team, saying he's always motivated to play for India.