The 20-year-old arrived at the Den in September and has been instrumental in the Lions' rise up the Championship.
Wood has netted seven times, including the winner against Leeds on Sunday which extended their unbeaten run to 10 games.
The deal is a massive boost for the Lions who expect to be without striker Darius Henderson for at least the next two matches with a hamstring strain.
"We're pleased with what Chris has done," said Jackett. "He's worked hard as part of the group.
"Personally I think he has benefited from playing with the likes of Darius and Andy Keogh."
Millwall go to Blackburn on Saturday followed three days later by a trip to Wolves.