Buck joined the County on a three-year deal from Lancashire last summer and enjoyed an impressive first season.
He took 36 wickets in eight County Championship Division Two appearances in 2017, at an average of 21.39.
Buck bagged three five-wicket hauls in four-day cricket, with his career best figures of six for 34 coming against Durham.
He also contributed some handy runs with the bat, racking up 201 in total.
But he will now definitely miss the season opener against Middlesex at Lord's, which starts on April 13.
"The biggest disappointment at the moment is Nathan Buck, who has picked up an Achilles injury and is going to miss the start of the season," said Northants head coach David Ripley.
"That's a shame because he's had a good winter, he's been bowling well in pre-season and it's a shame he's not going to make the cut for the start of the season.
"I reckon he's going to be out for four to six weeks so I would think we'll see him back early May time."
Rob Keogh has been nursing a back problem, but Ripley believes the all-rounder will be fit to face Middlesex.
"Rob Keogh's had a little bit of a back injury but we're hopeful he's going to be available for that first game," Ripley said.