Vettori was helped from the field after his right knee dug into the ground while attempting to take a catch in New Zealand's Cricket World Cup group match against Pakistan.
New Zealand won the match by 110 runs.
Clinical tests and a scan have showed that Vettori had a mild strain of his post cruciate ligament and he is likely to take part later in the tournament.
"It's a bit stiff and sore the last couple of days and 13 hours of travel never helps anyone," Vettori said.
"It felt a lot better today and it's a lot easier to walk. There's still quite a lot of swelling so as soon as that comes down I'll be back into it."
Vettori said the injury now needed rest and would miss the match against Canada on Sunday but he was targeting the final match of group play against Sri Lanka on March 18.
"I really want to play in that Sri Lanka game heading towards those quarter finals," he said.
"The crucial thing is I should be able to continue on with the tournament.
"I suppose now for me it's about symptoms and the sooner those symptoms dissipate the quicker I can get back on the field, which is what everyone wants," Vettori said.
