At the current sales pace, it would take 4.8 months to exhaust the supply of homes for sale. That's the shortest such span since September 2005.
At the same time, more people are looking to buy or rent a home after living with relatives or friends during and immediately after the Great Recession.
As low supply and rising demand push up prices, builders will likely be encouraged to start work on more homes in coming months, economists said.
"That's a good reason to feel optimistic about housing next year," said Patrick Newport, an economist at IHS Global Insight. "We just don't have enough homes right now, and we need to start building."
Builder confidence rose in December for a seventh straight month to the highest level in more than 6½ years, according to a survey released Tuesday by the National Association of Home Builders/Wells Fargo.
The pace of home construction slipped in November, but it was still nearly 22 percent higher than a year earlier. Builders are on track this year to start work on the most homes in four years.
Economists note that the increase in building should lead to more construction jobs, though it hasn't yet done so. That could mean more construction hiring is coming.