The 29-year-old St Asaph-born frontman, who has scored nine league goals this season, suffered damage to his medial knee ligaments in the 6-0 Welsh Cup win over Bryntirion Athletic at the start of December.
TNS manager Carl Darlington has backed Alex Darlington to step up and fill Williams’ boots.
"Matt and Alex are very similar in the way they play," he said.
"Alex has had a run of three games now and he’s been our most consistent player in those matches.
"He’s raised his standards and that’s what we expect week in week out. I’ve got massive faith in his ability."
Williams is a Wales Under-21 international who joined Manchester United as a 16-year-old.
He spent five years at Old Trafford without ever breaking into the first team and played for Notts County, where he made 26 appearances, Tamworth and Burton Albion before joining Rhyl in July 2008.
After two seasons at Belle Vue, where he top-scored in 2009/10, Williams left to join The New Saints in June 2010 and again topped the goal charts last season with 19 in the Welsh Premier.