The PMI, which indicates business growth with numbers above 50, dropped from 50.9 to 49.3 in the month, its lowest level since August.
Both house building and commercial construction slowed, the report said. For commercial construction, the decline was the steepest since December 2009.
Civil engineering activity rose in the month, posting its highest level in seven months. But new orders for construction projects fell at the fastest pace in nearly 3 1/2 years.
The numbers make 2012 "a year to forget," Markit senior economist Tim Moore said in a statement Tuesday.
"November's PMI survey suggests that construction output has yet to hit rock bottom," he said.