An algeacide will take care of it. The Borgs will carry it. Garden centers. Even hardware stores.
Ron

Ron, is the algaecide safe for brick? I have the same thing creeping up my brick. Thanks,
Fuzzy

I would look at the info on the container to verify. They use it on brick walks around here. Algae and moss grow in the paver joints that are in shade alot of the day.
Ron

bleachis great for that too,.

Thanks guys, and thanks to the original poster for bringing up the question.
Fuzz

The green stuff growing on the brick sounds like moss. Moss in lawns is killed using, ferrous sulfate and ferrous ammonium sulfate, including Moss-Out, Moss-Kil, Rid-Moss. It sounds safe for using on brick without damageing it.

One other point - if the conditions that encouraged the moss growth don't change, it will grow back. I'm guessing the area it's growing in is shady. The shade combined with humidity/dampness are prime conditions for it to do well.

It could be lichen which is harmless.