In 1975, Muhmenthaler transferred with a two-year contract to FC Basel. He made his team debut in the 5–1 home win against Grasshopper Club Zürich and Muhmenthaler scored three of the goals. He was part of the title winning team in the 1976–77 football season. During a cup match in February 1976, he suffered a meniscus rupture. Nevertheless, Basel extended his contract despite the fact that Muhmenthaler had to undergo three operations within the following two years. Muhmenthaler reached his third Uhrencup Final with his third club in 1977 but was unable to repeat the success, the final ended in a 6–1 defeat against Neuchâtel Xamax. Reaching the final again in the next year, Basel won the 1978 Uhrencup 2–1 against the same finalists.