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Probably not this one, since it's quite recent, but 'Hey Ya', by Outkast? https://www.youtube.com/watch?v=3ytxZdmSqr0
2:50 has 'Shake it, shake shake it' repeated.
“Shake It” by Ian Matthews? It was a US top 20 hit in 1978. https://www.youtube.com/watch?v=mSIGdNpTIEE
Jackson 5's "A,B,C"?
shake your groove thing by peaches and herb? https://www.youtube.com/watch?v=EtaZ48fERfc
David Bowie's "Shake It" (1983)? https://www.youtube.com/watch?v=GU1Jv7kz_60
It's a very recent song, but "Shake It" by Metro Station, maybe?
"Shake Your Thang" by Salt 'n Pepa?
Otherwise known as [Smashing Melons 42].
The Cars. "Shake It Up"
Is it kind of an old-school dance song? MC Shy D had a song called "Shake It" that went "Come on! Shake shake it!"
Baby Got Back? It goes "Shake it, shake it, shake yo' healthy butt"
"Shake it-a baby now (shake it-a baby) twist and shout (twist and shout) come o- come o- come baby now (come on baby) let me work it all out (work it all out)"
The Animals did a version of the John Lee Hooker song Boom Boom that had them adding several "shake it" lines in it details here. That version (by the animals) had a cover version done The Oak Ridge Boys in 2009.
What about Cabaret Voltaire- I want you?
I remember a song with the words "Shake it!, Shake it!" in it, it was probably made in the 70's/80's