Greenhouse Permit?

Not necessarily if it’s what’s considered a portable structure (which a lot of backyard DIY Greenhouse kits are)

Your best bet ...

Call your Municipality and have an City Bylaw Officer or Building inspector to pay a visit / take a look

AN ASIDE ... I think we had another RFDer posting here recently saying this was their exact plan
Erecting a greenhouse on their deck
(I will see if I can find that thread )
And for the record we told him that he may not require a permit, greenhouses don’t usually need one... but as it is a structure attached to another structure (such as a house, deck, fence or shed) it just might and he should check with his Municipality BEFORE he buys one or installs it

Here it is, from Mid March
sturdy-glass-greenhouse-backyard-2361814/#p32275566

EDIT / ADD - Some bylaws also relate to height of structures (eyesore / lack of privacy)
So if it overlooks your yard perched atop an existing deck
THAT MIGHT BE THE ISSUE that needs to be looked at

Check the bylaws in your area. In Mississauga the 8x8 to 10x10ft discussed in the other thread won’t be a bylaw violation or need a permit because the size is under the limit. Now if the roof peaked higher than 10 ft from grade it then becomes a bylaw violation.

In Mississauga a greenhouse larger than the size above is considered an accessory structure which has its set of size and high requirements based on lot size. The green house is grouped with other accessory structures like pergolas, gazebos, 3 season sunroom and kids play equipment.