Ali G, The Kumars At Number 42, Goodness Gracious Me and Banzai offend some of the racial groups they portray, according to new research.
The Broadcasting Standards Commission found Asian groups find the mocking of their culture in such shows "inexcusable".
Its research found a general acceptance that minorities could go further than white people in such parodies, but there is still the risk of offence.
"The fact these shows are produced by Indian people made no difference to the offence caused," the report said.
However, Indian sub-continent viewers agreed these shows meant Asians were far better represented in British comedy than in other genres.
Research also investigated the furore surrounding Ali G, played by white Jewish comedian Sacha Baron Cohen.
One black viewer said: "If you put it in reverse, imagine a black man going on there and acting like a Jew. There would be an uproar."
But many felt Cohen could get away with the act because he too was from a minority group.
The study said: "They enjoyed the way in which he is considered to highlight the ridiculousness of establishment figures, particularly in the interviews he conducts."