The white female rhea, nicknamed Snowflake, was spotted in North Boarhunt. It is thought she escaped from a private collection.
Police, the fire service and members of a specialist team from Sparsholt College helped catch the bird.
She is being kept at the college while she waits to be reunited with her owner.
A man spotted the bird at 12:30 BST on Thursday in his garden.
Chris Mitchell, centre manager at Sparsholt College, said: "Working with animals, we're accustomed to unusual conversations involving out of the ordinary situations.
"However it did catch me slightly off guard when we had a call from the Hampshire police control room declaring that there was a large bird in a front garden in North Boarhunt and could the college assist."
A large bird native to South America has been captured in a garden in Hampshire after fleeing from its owner.