This page explains in detail the interactions between the Pikmin series and the Zelda series.
The Legend of Zelda: The Wind Waker
December 13, 2002
Comparison between the Goddesses statues and the three original Pikmin.
Pikmin
Zelda
The three statues found on the Triangle Islands (before turning into the statues of the Goddesses), are likely based on the titular creatures from Pikmin, since they all have a part on top of their heads, like Pikmin have a steam and leaf on top of their heads, and each one of them even has the distinct feature of the colored Pikmin it correspond with: Din's statue (red) has a long nose, like the Red Pikmin, Nayru's statue (blue) has a mouth, like the Blue Pikmin, and Farore's statue (green) has ears, like the Yellow Pikmin (there's no green Pikmin).
The Legend of Zelda: The Minish Cap
January 10, 2005
Pikmin
Zelda
The Powaru enemy was renamed Puffstool in the international version of the game, which corresponds to the english name of an enemy from Pikmin (that was called Bokenameko in Japanese). Since they're both walking fungus with a red cap, it's possible that this was a reference, but it might just be a coincidence.
Some even consider them the same enemy, but since their original name was different we can assume that they are supposed to be two different enemies. Also they behave differently and there are differences in their look.
The Legend of Zelda: Ocarina of Time 3D
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June 16, 2011
Pikmin
Zelda
It's been reported by some players that the Nintendo 3DS remake of Ocarina of Time would feature plants from the Pikmin series, or at least based on those.
License
Copyrights for both series are held by Nintendo.