Wilson's absence is a major blow for the Tyneside club who, like Leeds, will look to the Elland Road clash on January 22 as one of the more favourable opportunities to pick up points amid a relegation struggle.
The Magpies are 19th in the Premier League table, two points adrift from safety after waiting until December to claim their first win of the season.
It was Wilson's 40th-minute strike, his sixth goal of the season, which bagged Newcastle three crucial points during a 1-0 home victory over fellow strugglers Burnley in December.
No one in Howe's side has been more prolific in front of goal, but now the Magpies will miss their top-scorer for a lengthy spell, which includes Newcastle's trip to Elland Road later this month.
After the 29-year-old suffered a calf injury during the Magpies' 1-1 draw with Manchester United in December, Howe confirmed on Saturday that the 29-year-old's lay-off will extend into March.
“He had a scan yesterday because there was a slight doubt in the first scan as we had to let it heal a bit further," Howe said.
“We think he is going to be out for eight weeks.”
Howe's revelation followed Newcastle's shock FA Cup third round exit at the hands of League One side Cambridge United on Saturday.
Left without a recognised senior striker, the Magpies boss started Allan Saint-Maximin as a central attacker and tried Ryan Fraser, Joelinton and Jacob Murphy out as number nines to no avail as Newcastle drew a blank at St James' Park.
Though a star turn by Yellows 'keeper Dimitar Mitov stopped nine on-target shots to keep the underdogs in the tie, Newcastle's 14 misfired efforts were a source of worry for Howe.
“A lot of our play was OK up to the last part. And the quality was missing for us today," Howe said.
“I thought we put a huge amount of crosses into the box with very limited success.
"We did create chances but didn’t take them.
“We prepared and the players desperately wanted to win but we were just not good enough in front of goal.”