Patel was reported by umpires Steve Bucknor of the West Indies and Simon Taufel of Australia after the ill-tempered second day's play at the Gaddafi stadium on Tuesday.
Match referee Ranjan Madugalle summoned the umpires, Patel, Indian captain Rahul Dravid and coach John Wright for a hearing late on Tuesday night where video footage of the day's play was viewed.
Patel pleaded guilty of the charge, according to Indian team manager Ratnakar Shetty, and Madugalle slapped the fine on the 19-year-old playing his 15th Test.
Patel will lose around 2,000 dollars.
The Indians appeared disappointed when numerous appeals were turned down by Bucknor and Taufel against the Pakistan batsmen, who ended the second day at 355 for three in reply to India's modest 287.