Both stars have confirmed the split, with Gummer's representative telling "It's very amicable", reported Us magazine.
The couple first met while performing together in the 2008 Broadway production of "Les Liaisons Dangereuses".
In 2009, Gummer gushed to the media that Walker had surprised her with a custom-made engagement ring.
"He did it on one knee! My mom loves him!" she had said at the time.
The pair tied the knot in July 2011 at her family's Connecticut estate. The 29-year-old "Side Effects" actress is the second eldest of Streep's four children with husband Don Gummer.