Fatullah will host the test, which will be the first between the sides since January 2010.
A limited-over international series against India is considered a money-spinner and accordingly all three matches, to be held in Mirpur, have been allotted a reserve day due to the threat of monsoon rains.
Sureh Raina led India to victory in Bangladesh last June during a three-match ODI series, which saw the third contest in Mirpur washed out due to heavy rain.
The teams have faced off in seven previous test matches with India winning six and the other contest ending in a rain-affected draw.
Bangladesh are currently hosting Pakistan, with the teams level in a two-match test series after last week's drawn opener. The home side beat the tourists 3-0 in an ODI series prior to the first test and also won a one-off Twenty20 international.
(Reporting by Sudipto Ganguly; Editing by John O'Brien)
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