Abhishek Sharma was born on 4 September 2000 in Amritsar, Punjab, to Raj Kumar Sharma and Manju Sharma. He has two elder sisters. He studied at Delhi Public School, Amritsar.
He is a childhood friend of India batter Shubman Gill; the two opened the batting together for Punjab at the Under-14 level. Former India all-rounder Yuvraj Singh mentored him and worked on his batting during the COVID-19 lockdown.
In the 2015–16 Vijay Merchant Trophy (Under-16), he scored a century on debut and finished with about 1,200 runs at an average of 109.09. He captained India Under-19 to victory at the 2016 U19 Asia Cup, winning Player of the Match in the final, and was a member of India's 2018 U19 World Cup winning squad.