This in from Notify NYC:
Notification issued 12/20/13 at 12:00 PM. Due to necessary roadway repairs, the Manhattan-bound Brooklyn Bridge will be closed to vehicular traffic overnight during the following dates/times: Saturday 12/21 from midnight to 7 AM, Sunday 12/22 from midnight to 9 AM, Monday 12/23 from midnight to 6 AM, and Monday and Thursday nights, 12/23 and 12/26 from 11 PM to 6 AM (Friday morning, 12/27). Consider alternate routes during closures, including the Manhattan Bridge.
Note that there is no closure from midnight to early morning, or at any time, on Christmas day (Wednesday, December 25).