David Monro was born in Edinburgh, Scotland, on 27 March 1813, the seventh of twelve children of Maria Carmichael-Smyth, and her husband, Alexander Monro, the third-generation holder of the chair of anatomy at the University of Edinburgh. A foundation pupil at Edinburgh Academy, Monro went on to the university, graduating Doctor of Medicine in 1835. He studied in Paris, Berlin and Vienna, then began practice in Edinburgh.
In 1841 Monro bought four allotments of land in the proposed Nelson settlement in New Zealand and sailed for Melbourne, Australia, as surgeon on the Tasmania in the company of his friend Edward Stafford. He spent some time with a brother who had settled in Victoria, then sailed to New Zealand on the Ariel, arriving in Nelson in March 1842. Monro took up the life of a pastoralist in Nelson and Marlborough. In 1844 he was a member of Frederick Tuckett's expedition seeking a site for the proposed Presbyterian settlement of New Edinburgh. Monro married Dinah Secker at Waimea on 7 May 1845; they were to have five sons and two daughters.
Monro's political career began in 1843 when, in the aftermath of the Wairau incident, he and Alfred Domett were chosen to put the views of the Nelson settlers before the acting governor, Willoughby Shortland. Monro also actively opposed the attempt to make the Nelson settlers bear a portion of the debts of the New Zealand Company. In 1849 he was appointed to the Legislative Council for the province of New Munster. He attended the session in Wellington that year but resigned his seat in 1850 because of a dispute over the way in which the governor, George Grey, had appropriated revenue without summoning the Council. In 1851 and 1853 Grey invited Monro to accept appointment to the Legislative Council; he declined, on the second occasion because he believed that under the new constitution the Council should have been an elective body. Monro was elected to the House of Representatives as member for Waimea West in 1853; he also represented Picton from 1858 to 1866 and Cheviot from 1866 to 1870. He was a member of the Nelson Provincial Council from 1853 to 1864, and was narrowly defeated in 1856 for the superintendency; in this contest Monro opposed the ex-Chartist John Perry Robinson, spokesman for workers and small landowners.
Monro's belief in strong central government led him, in 1854, to turn down acting governor Robert Wynyard's invitation to join the Executive Council; acceptance would have meant serving with the Canterbury provincialist James Edward FitzGerald. At the opening of the third parliament on 3 June 1861 he was elected speaker of the House and retained that post through 10 sessions. As speaker he succeeded in maintaining the traditional dignity of the House and its chair. His most controversial decision was the exercise of his casting vote to unseat the Fox ministry in 1862. Later in the session he ordered the clock of the House put back so that a bill could be sent to the Legislative Council in due order.
Monro was knighted in 1866. On 13 September 1870, when the House was prorogued, Monro announced that it would be his last session as speaker. William Fox as premier failed to move a vote of thanks for Monro's long service. Monro did not forgive the slight and stood again in the 1871 election. He was declared elected for Motueka on the returning officer's casting vote, but was later unseated by an electoral petition decided by a committee of the House. This committee had a government majority and made legally dubious findings. Fox then succeeded in blocking the House's desire to have Monro appointed to the Legislative Council. In 1872 Monro was elected for Waikouaiti and voted for the motion of no confidence which temporarily ended the Fox ministry. He resigned in 1873.
Monro practised medicine only incidentally in New Zealand. In addition to his political career he was a leader of the Nelson pastoralists, a justice of the peace, president of the Nelson Institute, a trustee of the Nelson Trust Funds, and a foundation member of the council of governors of Nelson College. David Monro died in Nelson on 15 February 1877, and Dinah Monro died in 1882. Their eldest daughter, Maria Georgiana, married Sir James Hector, and a son, Charles, introduced rugby football to New Zealand in 1870.