On 10 November 1734 in Potsdam, Sophia Dorothea married her Hohenzollern kinsman Frederick William, Margrave of Brandenburg-Schwedt, son of Philip William, Margrave of Brandenburg-Schwedt, and Princess Johanna Charlotte of Anhalt-Dessau, daughter of John George II, Prince of Anhalt-Dessau.

They had five children: Frederick William was 19 years older than the princess and he was called the "mad Margrave" because of his pranks and rude manners.

They only reconciled during Sophie's terminal illness, when she died in the Margrave's arms.

She did not, reportedly, have the same spiritual interests of her siblings, Frederick the Great, King of Prussia and Louisa Ulrika, Queen of Sweden.

The Margraviate of Schwedt was only a small holding, but enjoyed a prosperous economy due to immigrant Huguenots.