Robinson, now 27, has been suspended from all international cricket pending the outcome of a disciplinary probe, the ECB said.
But Mr Dowden asked the board to “think again”, saying: “Ollie Robinson’s tweets were offensive and wrong.
“They are also a decade old and written by a teenager.
“The teenager is now a man and has rightly apologised. The ECB has gone over the top by suspending him.”
Sussex seamer Robinson will miss the second Test against New Zealand.
‘It’s not acceptable within our game’
England captain Joe Root said on Sunday he “couldn’t believe” what had emerged on Wednesday and added “it’s not acceptable within our game”, before the ECB statement confirmed Robinson would leave the team bubble.
“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,” the statement said.
“He will not be available for selection for the LV= Insurance second Test against New Zealand starting at Edgbaston on Thursday June 10. Robinson will leave the England camp immediately and return to his county.”
After the first day’s play between England and New Zealand, Robinson read from a prepared statement to say he was “embarrassed” and “ashamed” of the offending posts.
They came to light hours after England had marked the first Test of the summer at the Home of Cricket by sharing a “Moment of Unity” alongside the visiting Black Caps before play, taking a stand against several forms of discrimination.
Robinson apologised to the media and to his team-mates and while Root believes the contrition is heartfelt, the England captain says everyone within the game can take lessons following what has transpired.
Root said: “It’s not acceptable within our game. We all know that.
“He addressed the dressing room straight away. He fronted up to it. He showed a lot of remorse from that point onwards. You can see it’s very genuine from how he’s been around the group and the team.
“And I think it’s a great lesson for everyone within our game that we can all do more.
“We all have to keep looking to educate ourselves, trying to better the environment for everyone, trying to be as inclusive as we can, keep making everyone feel comfortable to play what a wonderful sport we have.”