The Gunners recently won their first Premier League title in 22 years, but Terry believes they need an upgrade on striker Viktor Gyokeres - and he's suggested Kane, the former Tottenham captain, would be the ideal signing.
During an appearance on Piers Morgan Uncensored, Terry told the host: "I actually feel you guys are missing out on a top striker that’s going to get you 25, possibly 30 goals a season.
"You look at all the best sides over the past 20 years, Henry done it, Rooney done it, Drogba, every team had that one player up front who produced those goals."
Terry, 45 - who captained Chelsea to multiple Premier League titles during his own playing days - then suggested a shock name as a possible replacement for Gyokeres.
Asked who Arsenal should sign this summer, Terry replied: "Harry Kane.
"I’m actually not sure who would want to go to Arsenal, that’s the issue.
"Worryingly, I think you guys for the next two or three years have got the opportunity to dominate."
Terry also reflected on Chelsea's underwhelming season in the Premier League.
The former captain expressed his disappointment over the Blues' campaign - but he's hopeful that Xabi Alonso, the new coach, might turn things around.
He said: "It’s not been ideal and it’s probably been the worst season I’ve seen since I retired, to be honest.
"I think ownership and sporting directors went down the role of bringing in players who are young and maybe hungry, but my view has always been we need experience around this group of young players, I still think we desperately need that.
"I’m hoping with Alonso coming in, after the disastrous season we’ve had, I think he’s a really good signing and actually I don’t think we could’ve got any better in the position we’re in.
"He’s got a great football brain, I’ve come across him, played against him for many years, I think he’s going to sign some experienced players. I think if he gets the freedom to sign the players he wants, we could move in a direction that’s better for us."