Kulkarni experienced pain in his toe last evening and was taken for a scan, following which he was ruled out of Mumbai's Ranji Trophy game against Delhi, which started today.
The Mumbai bowler had earned his maiden national, limited-overs call-up after being named in the 15-member squad on Tuesday.
Vinay Kumar had been dropped from the ODI squad against West Indies after his poor showing in the limited-overs series against Australia recently.
Although Vinay finished with eight wickets in the series, he conceded 345 runs in five games at an average of 41.87, including figures of 102 for 1 in nine overs during the final ODI in Bangalore.
The first ODI between India and West Indies will be played in Kochi on November 21, while the remaining two ODIs will be played in Visakhapatnam and Kanpur on November 24 and 27, respectively.