The 20-year-old centre-back arrived from Liverpool on Tuesday and was an unused substitute in the 2-2 draw against Scunthorpe, which left the Shrimpers lying in seventh place in Sky Bet League Two.
Sokolik, who joined the Reds from Banik Ostrava in 2009, impressed Brown during a trial period and with his performance in a friendly against Colchester.
"I was very impressed with Jakub in the game against Colchester and in training last week," Brown told the club's website.
"We've had a number of injury problems in the centre of defence this season and he'll come in to play a big part between now and the end of the season.
"He's a young lad, but Liverpool have given him a good education. I'm sure he'll come here and make an impact."
- Sports & Recreation