A number 7 envelope looks very close - just a quarter inch wider.
These have the triangle flap style but I think that looks nice for cards and they might do the job for you. The
number 7 coin envelope has the open end flap style and is also close in size (it's a quarter inch shorter so only 6 1/2).
I have no affiliation with the company, I just did a quick google and turned these up as examples, you may well find a similar assortment at a decent stationery store.
HTH!