The Tamil Nadu right hander has not played any competitive cricket since suffering a wrist injury after the Australia series, which Virat Kohli's men won 2-1.
BCCI, in a press release stated that Vijay "has complained of pain in his right wrist while playing a preparatory match".
The BCCI medical team has advised Vijay to continue his rehabilitation program.
Shikhar Dhawan has so far played 23 Tests and scored 1464 runs at an average of 38.52. Dhawan last played a Test during India's home series against New Zealand in Kolkata in October 2016.
India kick-off their Sri Lanka tour with the first Test at Galle on July 26. Following fractured left thumb Dhawan was ruled out of Test series against Kiwis.
The left-hander returned for the ODI series against England but he put on a fabulous show in the ICC Champions Trophy 2017. He was alo not considered for five-match Test series against England but made a comeback in the limited-overs series. This is the first time the two countries will be playing a full series (includes all three formats) in eight years.
After the Test series, India are scheduled to play five one-dayers starting August 20 before signing off with a lone Twenty20 on September 6. All the three Test matches will be played in Galle, Colombo and Kandy.