Friedrich I of Württemberg (19 August 1557, Montbéliard – 29 January 1608, Stuttgart) was the son of Georg of Mömpelgard and his wife Barbara of Hesse, daughter of Philip I, Landgrave of Hesse.

Several references are made to him in Shakespeare's The Merry Wives of Windsor, in which a series of anti-German jokes start with a horse theft, several references are made to German travellers in England and to a German Duke who is not expected to come to Windsor.

Frederick of Mömpelgard was heir apparent to the dukedom of Württemberg when he visited Windsor and other English cities in 1592. He developed a desire to be made a Knight of the Garter and solicited Queen Elizabeth for the honor repeatedly. After he had inherited the dukedom and become more prominent in affairs, she admitted him to the order. In a calculated slight, he was not informed of his admission in time to attend the investiture in spring 1597, the ceremony for which The Merry Wives of Windsor was written. Thus references to Mömpelgard's earlier visit and his not being in Windsor were jokes intended for the play's first audience, and appear in the First Folio edition of the play, taken from the first private performance, but not in the 1602 Quarto derived from public theatrical production.

In 1599, Frederick I issued an order that a new town should be established at the northern extremity of the black forest by the name of Freudenstadt. The aim was for the town to become the new residence of the Duchy of Württemberg as it was closer to Mömpelgard that the Württemberg capital Stuttgart. However, Frederick I died in 1608 and his plans never came to fruition.

The sons of Frederick I established the ducal house of Württemberg - Neuenstadt, a branch line of the House of Württemberg after a Fürstbrüderlicher Vergleich - a mutual agreement made between ducal brothers on 7 June 1617. The eldest son, Johann Friedrich, assumed barony over the Duchy of Württemberg while the second youngest son, Frederick Achilles, was bequethed Neuenstadt Castle and an annual endowment of 10,000 guilder.