As well as testing his left-arm off-spin, in which the index finger plays a key role, he also had two batting sessions on Monday.
Vettori was one of five players to arrive after the first two tour matches because of Indian Premier League commitments.
And he missed the final tour match at the Rose Bowl after suffering the injury at Chelmsford, leaving him unable to bowl in the second innings against Essex.
Speaking ahead of the first Test, England batsman Kevin Pietersen was full of praise for Vettori.
"Daniel is a good guy and world class when he is on top of his game," Pietersen told BBC Radio 5 Live.
"He's the best left-arm spinner in the world and is right up there with the guys who think so much about the game.
"Daniel has played for almost 11 years now so he has picked up so much experience and he thinks about every thing he does, every single ball that he bowls.
"He's a world class player and we're going to have to try and dominate him."
But for Vettori's injury, New Zealand's preparations have generally gone well, with a win against Essex sandwiched between draws against Kent and the England Lions.
There is only one other injury in the camp, with seam bowler Iain O'Brien hoping to recover quickly enough from a calf strain to be available for selection for Lord's.
Even if he was able to play, O'Brien would probably be overlooked, with Chris Martin, Kyle Mills and Tim Southee the likely first-choice seamers.
