Robinson made his England debut in this week’s First Test draw, impressing with seven wickets and an important 42 with the bat in the first innings.
However, a number of old tweets containing racist, sexist and homophobic comments emerged during the first day’s play.
The Sussex seamer “apologised unreservedly” in a statement on Wednesday evening, but he has now been suspended by the England and Wales Cricket Board pending a disciplinary investigation.
An ECB statement said: “England and Sussex bowler Ollie Robinson has been suspended from all international cricket pending the outcome of a disciplinary investigation following historic tweets he posted in 2012 and 2013.
“He will not be available for selection for the LV= Insurance second Test against New Zealand starting at Edgbaston on Thursday 10 June.
“Robinson will leave the England camp immediately and return to his county.”