Shanahan, 38, is a California lawyer and philanthropist who has never held elected office.
She leads the Bia-Echo Foundation, an organisation she founded to direct money towards issues including women's reproductive science, criminal justice reform and environmental causes.
Kennedy, a former Democrat, made the announcement in Oakland, California on Tuesday.
"Nicole and I both left the Democratic Party," he said.
"Our values didn't change - the Democratic Party did."
Without the backing of a party, he faces an arduous task to get on the ballot, with varying rules across the 50 US states.
Kennedy is picking a running mate now because about half of the states require him to designate one before he can apply for ballot access.
In advance of the event in Oakland, he and his aides circulated the names of several contenders, including celebrities with no experience in politics.
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