He was born in Halifax, England in 1740 and came to Quebec with his brother Benjamin around 1763; their brother Thomas joined them around 1769. They set up a fur trading company based in Montreal that traded in the Northwest, later partnering with Simon McTavish after Benjamin's death in 1787; both firms were part of the North West Company. He married Charlotte, the daughter of surgeon Jean-Baptiste Jobert, in 1779. Frobisher was named a justice of the peace in 1788. He was elected to the 1st Parliament of Lower Canada for Montreal East in 1792. Frobisher retired from the company in 1798. He was secretary for the Beaver Club at Montreal. Frobisher was part-owner of the Batiscan Iron Works and, with his partners, purchased the seigneury of Champlain. He also had extensive land holdings himself. Frobisher built a large residence on his estate, Beaver Hall, outside Montreal and he also owned a large house in town. He served in the local militia, becoming major by 1806.
He died at Montreal in 1810.
His son Benjamin Joseph also entered the fur trade and served in the legislative assembly.