Her Highness Princess Frederica Louisa Carolina Sophia Alexandra was born at Hanover, the fifth daughter of Duke Karl II of Mecklenberg-Strelitz (1741-1816) and his first wife, Frederica (1752-1782), the daughter of Georg Wilhelm, Landgrave of Hesse-Darmstadt. Her father assumed the title of Grand Duke of Meckelbenberg-Strelitz on 18 June 1815. Duchess Frederica was the niece of her future mother-in-law, Queen Charlotte (formerly Princess Charlotte of Mecklenburg-Strelitz).
Princess Frederica married firstly His Royal Highness Prince (Friedrich) Ludwig of Prussia (5 November 1773-23 December 1796), the younger son of King Friedrich Wilhelm II of Prussia, on 26 December 1793 at the Royal Palace, Berlin. The couple had three children:
- Prince Friedrich of Prussia (1794-1863); married Princess Louise of Anhalt-Bernbourg (1799-1882).
- Prince Karl of Prussia (1795-1798).
- Princess Frederike of Prussia (1796-1850); married Leopold IV, Duke of Anhalt-Dessau (1794-1871).
- Princess Sophia zu Solms-Braunfels (b. and d. 1799).
- Prince Friedrich Wilhelm zu Solms-Braunfels (b. and d. 1800)
- Prince Wilhelm zu Solms-Braunfels (1801-1868); married Maria, Countess Kinsky von Wchinitz und Tettau (1802-1892).
- Princess Augusta zu Solms-Braunfels (1804-1865); married Albert, Prince (Prinz later Fürst) von Schwartzbourg-Roudolstadt (1798-1869).
- Prince Alexander zu Solms-Braunfels (1807-1867); married Louise, Princess (Fürstin) von Landsberg-Velen (1835-1894).
- Prince Karl zu Solms-Braunfels (1812-1875); married Sophie, Princess zu Löwenstein-Wertheim-Rosenberg (1814-1876).
- Princess Frederica of Cumberland (stillborn on 27 January 1817).
- An unnamed stillborn daughter (April 1818).
- Prince George of Cumberland (later King George V of Hanover) (27 May 1819-12 June 1878).