Sachin, 49, who retired in 2013 as international cricket’s most prolific batsman with 100 centuries, played six seasons with Mumbai Indians and is currently the team’s mentor.
In his IPL debut, 23-year-old Arjun opened the bowling against Kolkata Knight Riders, conceding 17 runs in the first two overs before being taken off.
“Arjun, today you have taken another important step in your journey as a cricketer,” Sachin Tendulkar wrote on Twitter.
“As your father, someone who loves you and is passionate about the game, I know you will continue to give the game the respect it deserves and the game will love you back.
“You have worked very hard to reach here, and I am sure you will continue to do so. This is the start of a beautiful journey. All the best.”
In a post-match interview, the Tendulkars reflected on the historic day with Arjun saying, “It was a great moment, it is always special to play for the team I have supported since 2008.
“And it was very nice to get the cap from the captain of MI and the Indian team.”
Sachin added that he had not watched his son play before: “This was a new experience for me because ‘til now I have not actually gone and watched him play. I just wanted him to have the freedom to go out and express himself and do whatever he wanted to.
“And today also, I sat in the dressing room because I didn’t want him to let him move away from his plans and start looking at the mega screen here and suddenly realize that I was watching there. I was inside.
“It is a different feeling because 2008 was the first season for me and 16 years down the line, he plays for the same team. Not bad,” Sachin concluded.