The bird was spotted walking down the path on Tuesday afternoon before crossing the road.
The flamingo made its own way back inside the zoo and was found by keepers on a grass lawn within the grounds.
The zoo said a gust of wind carried the bird outside of its enclosure, but following a health check she was returned unharmed to the rest of the flock.
Videos showing the flamingo outside the zoo with a cyclist riding past have been shared by more than 1,000 people on Facebook.
Kayleigh Pritchard posted the videos saying: "Even the flamingo is sick of isolation."
A spokeswoman for Dudley Zoo said: "During the afternoon of Tuesday 14th April the flamingos were in their outside enclosure when the weather suddenly turned blustery and a gust of wind carried one of the flock out of its enclosure.
"Thanks to a phone call from the public, keepers quickly located the bird and following a quick health check she was returned unharmed to the rest of the flock.
"When the flamingo was located she on a grass lawn within the zoo grounds and it was only later that we found out that the flamingo had gone across Castle Hill road before heading home of her own accord.
"Although the flamingos wings are clipped so they cannot fly they are still able to glide. The management team will investigate the best option to fully net over the flamingos existing outdoor area.
"We are pleased to confirm that the flamingo suffered no ill effects and is happily eating her breakfast this morning."
One of our flamingos didn’t stick to the Stay Safe, Stay Home message and decided to take her daily exercise via Castle Hill!— Dudley Zoo (@dudleyzoo) April 15, 2020
Our keepers were on the scene within minutes and safely returned the flamingo back to their enclosure where she is now once again self-isolating! pic.twitter.com/ZV3vWVqgjQ