The Anfield club rejected the Gunners bid of £40 million plus £1 for the wantaway striker and the American was clearly not impressed.
Henry, who as owner of the Boston Red Sox was one of the pioneers of the 'Moneyball' movement of player evaluation, wrote on his twitter page: "What do you think they're smoking over there at Emirates?"
What do you think they're smoking over there at Emirates?
— John W. Henry (@John_W_Henry) July 24, 2013
The tweet spread like wild fire and had been retweeted 7,500 times just half an hour after it had been published.
The Gunners made an offer of one pound over the £40m mark in an effort to trigger a clause in the Uruguayan's contract.
Under the terms of the deal that Suarez signed in August last year, any bid over that figure would compel Liverpool to consider the offer and inform the player, although the Anfield club has again decided to reject Arsenal's advances.
Suarez is expected to be officially informed of Arsenal's bid after Liverpool's match against the Melbourne Victory on Wednesday.