Vijay sustained a wrist injury during the home Tests against Australia, playing three of the four matches before revealing he was severely hampered by a fracture that required surgery and forced him to sit out the Indian Premier League.
The two left-handers and KL Rahul, also returning from a shoulder injury, will be India's opening options for the three Tests beginning July 26 in Galle.
The left-handed opener has so far played 23 Tests and averages 38.52.
Vijay had suffered a wrist injury during Australia's tour of India, and this news will be another setback for the opener, who was looking to perform well in the island nation.
Fresh from an extraordinary ICC Champions Trophy 2017 edition, Shikhar Dhawan has found a place in the 16-member squad for Sri Lanka tour, where India will play 3 Tests.
Having been ignored for the Test series, Dhawan is now holidaying in Disneyland with his family.
The right-hander has been asked to continue with his rehabilitation program after complaining of wrist pain during a match.
With Abhinav Mukund already in the squad, it will be interesting to see if Dhawan does indeed feature in the Test series or is just there as a back-up. The Virat Kohli-led Team India departs for a full-fledged tour consisting three Tests, five ODIs and a one-off T20 global on July 19. It was India's first Test series win on Sri Lankan soil in 22 years.