Monro was born in Edinburgh, and graduated as a Doctor of Medicine from Edinburgh University in 1835. After first studying for a time in Paris, Berlin and Vienna, Monro established a medical practice in Edinburgh. In 1841, however, Monro bought land in the planned settlement at Nelson, New Zealand. He arrived in Nelson the following year.
In 1843, following the so-called Wairau Massacre, Monro was chosen (along with Alfred Domett, later to become Premier) to present the Nelson settlers' views to Willoughby Shortland, the acting Governor. Partly as a result of this attention, Monro was appointed to the Legislative Council of the Province of New Munster in 1849, but resigned after a dispute with Governor George Grey.
In 1853, Monro was elected to the 1st New Zealand Parliament, representing the seat of Waimea. He was re-elected in the same seat for the 2nd Parliament. At the beginning of the 3rd Parliament, to which Monro had been elected as representative of Picton, he was selected as Speaker. He is generally regarded as having conducted this duty "with dignity", although his use of the Speaker's casting vote to unseat Premier William Fox in 1862 was controversial. Monro remained Speaker until 1870, when he announced that he would step down. William Fox, who was once again Premier, failed to move the traditional vote of thanks.
Monro contested the Motueka seat in the 1871 elections, and was declared elected. A subsequent petition, however, overturned this result. The committee that made the ruling had a government majority, and some of its findings have been deemed "legally dubious" - many believe that the decision was taken for political reasons. Furthermore, a proposal to appoint Monro to the Legislative Council was blocked by Fox. Monro nevertheless succeeded in re-entering Parliament through a by-election in Waikouaiti. After the Fox government had been defeated, Monro resigned again.