Shaha was a member of Nepal Prajatantrik Party 1948-1949. 1951-1953 he was the general secretary of Nepali Rastriya Congress. He then became general secretary of the joint Nepali Congress-Nepali Rashtriya Congress front until 1956. Shaha was Minister of Finance 1960-1964. In 1962 he became chair of the Constitution Drafting Commission. 1967-1971 he represented the graduate constituency in the National Panchayat. In the panchayat, he was one of the most prominent advocates of democratic reforms.
Shaha was the Nepalese ambassador to the United States and the Permanent Representative of Nepal to the United Nations UN 1956-1960. In 1961 Shaha was elected by the United Nations General Assembly to chair the International Commission for investigating the death of UN Secretary General Dag Hammarskjöld, who had suffered an air crash over Congo. Shaha was one of the candidates to succeed Hammarskjöld, but was defeated by U Thant. In 1962, Shaha was appointed special ambassador.
Shaha lectured in English and Nepali at Tri-Chandra College 1945-1948. During the period 1947-1948 he served as chief inspector of schools 1947-48.
Shaha served as visiting professor at the School of International Studies, Jawaharlal Nehru University, New Delhi, India in 1970. In 1971 he served as Regents' Professor at Berkeley University, USA. He was a Fellow at the Woodrow Wilson International Center for Scholars, Washington. D.C. and the East-West Center, Honolulu.