Henry has admitted he is impressed by Tottenham's recent rise but also warned there could be financially challenging times to come for the club with the development of their new stadium.
The former Gunners ace wrote in his 'Sunsport' column, 'If you want to be a big club, you have to act like a big club.'
'I know from my own experience it is so hard to compete financially when you are building a new stadium. What happened at Arsenal? Everybody left!'
Mauricio Pochettino's side finally confirmed their first signing of the summer on Friday. Colombian international Davinson Sanchez has joined Spurs in a deal worth £45m and will bolster the team's defence.
However, Henry believes this is only the start and the North London side must do their best to keep big players at the club.
'Signing Davinson Sanchez from Ajax is a start, but only a start... there are other areas that need improving,' Henry added.
'Kyle Walker is already gone, Danny Rose has talked about it (leaving) ... Eric Dier never denied anything about Manchester United.
'At some point if you don't match the wages on offer at other clubs or bring titles it's going to be difficult to keep Rose, Dier, Harry Kane and Dele Alli.'
Tottenham are gearing up to play their first game at temporary home Wembley against Chelsea on Sunday, and you can follow it live here.