Arsenal have had two offers for the 26-year-old forward turned down and Henry made it clear that any further bids from the North London club, or elsewhere, would be similarly rebuffed.
The American, whose reaction to Arsenal's second bid was to tweet, "What do you think they're smoking over there at Emirates?", said he was "unequivocal" that Suarez would not be leaving.
"We are not going to sell Luis," Henry, who also owns Major League Baseball's Boston Red Sox, told British newspapers.
"For all the top clubs it's extremely important (not to sell to a rival) but especially for Liverpool because we're not in Europe this year and have not been in the Champions League for a while.
"To sell to a rival for those positions, or one of them, would be ludicrous. Liverpool needs to be playing in Europe. It needs to be playing in the Champions League. That's what Liverpool football club is about."
Henry said offers from clubs outside the Premier League would not be considered because there was too little time before the end of the transfer window on September 2 for manager Brendan Rodgers to replace him.
"He won't be sold even if a foreign club comes in because we do not have time to sign a suitable replacement," Henry added.
"It's a football reason. It's not about finances. That's why at this point, so late in the window, with everyone who's already moved or isn't moving, we can't replace him. So for football reasons we can't sell, and especially to Arsenal."
"I think the issue has been resolved now. We have said 'no'. Luis will be a Liverpool player on September 3."
Suarez told Spanish sports daily Marca on Thursday that he wanted an "amicable agreement" to leave the club and thought a bid over 40 million pounds ($62.22 million) was enough to trigger a clause in his contract.
Arsenal's bid was reported in the British media to be just one pound over that threshold.
As well as being Liverpool's top scorer, Suarez has been involved in two major storms during his two and a half years at Anfield - his racist outburst at Manchester United's Patrice Evra and his biting of Chelsea's Branislav Ivanovic.
The club backed him during both incidents, despite much criticism, and Henry said that the memory of that solidarity, particularly in the Evra incident, added to the disappointment of the Liverpool fans.
"If you look at the full context of what's happened here it's jarring to all our supporters," he said.
"The club has stood by him so strongly at a time when you could question whether the club should have stood by him, but they did. I wouldn't say we regret that.
"The manager and his team mates were solidly behind him. They were out on the field that day. So we felt they knew more about what occurred than we did, on the field."
($1 = 0.6429 British pounds)
(Reporting by Nick Mulvenney in Sydney; Editing by Ian Ransom)
