Ahead of Saturday's match between Wolverhampton Wanderers and Liverpool, Burton was caught in off-air footage discussing with Sky Sports colleague Andy Gray the decision to allow Sian Massey to run the line for the game.
Burton said, "Apparently a female lino today, bit of a looker", to which Gray responded: "A female linesman?"
"He [a Sky Sports crew member] says she [Massey] is all right," Burton added, "Now I don't know if I should trust his judgement on that..."
Gray replied: "No, I wouldn't. I definitely wouldn't...I can see her from here," before adding: "What do women know about the offside rule?"
Burton had been due to appear in his usual touchline role on Sky's coverage of the Carling Cup semi-final second leg tomorrow night between Birmingham City and West Ham United.
However, it is understood that he will now be replaced for the game as Sky takes a hard line on what it views as unacceptable behaviour from its presenters.
Gray and Sky Sports anchor Richard Keys were stood down by Sky last night from presenting Bolton Wanderers' clash with Chelsea in response to their disparaging comments about Massey and West Ham vice chairman Karren Brady.
Keys apologised to Massey over the telephone on Sunday night, but he and Gray are still facing strong disciplinary action from Sky.
Yesterday, England captain Rio Ferdinand slammed the Sky Sports presenters for their "prehistoric" views on women officials and executives in football.