The right-arm pace bowler will need to undergo a brief period of quarantine on arrival in India.
Shami, 30, suffered a fracture on his bowling hand after he was hit by a ball from Australia pace bowler Pat Cummins.
He could not pick the bat and was in pain. It has been learned that scans have revealed a fracture on his hand, and as a result he will not participate in the last three Test matches to be played in Melbourne, Sydney and Brisbane.
"Shami has been advised six weeks of rest and he will be leaving for India on Wednesday," a source told IANS.
He should be fit by the end of January after undergoing the six-week rest period.
India's full series against England begins on February 5, with the first of the four Tests at MA Chidambaram Stadium in Chennai.
Shami's injury is a big blow during the ongoing tour of Australia for India who will also be missing skipper Virat Kohli, who is returning to attend the birth of his first child.
The pacer was one of India's bowling heroes during the last tour of Australia, picking 16 of the 48 wickets taken by India's pace trio comprising him, Jasprit Bumrah and Ishant Sharma.
In the calendar year 2018, the Bumrah-Shami-Ishant combine took 136 wickets together, considered a milestone for a trio, beating the haul of Michael Holding, Malcolm Marshall and Joel Garner (130 wickets in 1984). In fact, 45 of those 136 wickets came in the first three Tests in Australia in 2018.