Khizr Khan told a rapturous crowd that his son Humayun had sacrificed his life to save those of his fellow soldiers.
If it had been up to Mr Trump, he said, his son would not have been in America.
Mr Khan asked if Mr Trump had "even read the United States Constitution", and offered to lend him his copy.
Appearing on stage in Philadelphia with his wife, Mr Khan, 65, paid tribute to their son who was killed by a car bomb in 2004 at the age of 27.