Molyneux Shuldham was born in Ireland circa 1717, and was the second son of the Reverend Lemuel Shuldham, by his wife Elizabeth, daughter of Daniel Molyneux of Ballymulvy, of County Longford.
On 31 August 1739, he was promoted to be lieutenant of , one of the ships which went out to the West Indies with Sir Chaloner Ogle, and took part in the unsuccessful attack on Cartagena in 1741.