Unseeded Amritraj went down fighting 5-7, 4-6 against French 25th seed Edouard Roger-Vasselin in the second round.
Amritraj last played in a Grand Slam in 2002 when he made the US Open main draw as a wild card entrant.
Yuki Bhambri has already exited following his first round defeat.
Now India's hopes to see a player competing in the singles event of the first Grand Slam of the season are resting on Somdev Devvarman who will play his second round on Friday.
He is up against Germany's Tobias Kamke.