And what was the cause of this transition? Economic, cultural, legal?
Restrictions on wooden buildings were a common response to disastrous urban fires that had spread quickly. After the Great London Fire (1666), for example, the 1667 Rebuilding Act stipulated: "No man whatsoever shall presume to erect any house or building, whether great or small, but of brick or stone."
Well, everyone knew what the best practice was, but masonry houses are a lot more expensive than wooden ones, and so—to choose one example—Chicago in 1871 was a city of wooden houses, easily swept by a fire that destroyed a quarter of the city's buildings. A push by civic leaders to ban wooden buildings was strongly opposed by German immigrants on the North Side, who could build wooden houses for their own families, but not brick houses with the deep footings required. Elaine Lewinnek's book The Working Man's Reward credits this (and other Fire responses) with making Chicago among the most "suburban" cities in the world.
Large urban fires were unfortunately not uncommon well into the 20th century, when a combination of political will, advances in firefighting, and modern building materials coincided with growing wealth and lower density to make multiple-structure fires rare.
Many urban buildings are still constructed with wood. Can you be more specific?