Puyol has had a string of issues keeping him off the field in recent years with knee operations, a fractured cheek and a dislocated elbow keeping him sidelined.
The veteran defender made just 22 appearances last season in all competitions and is yet to feature in the current campaign.
But Puyol is tipped to return to full training next week after successfully recovering from an operation to remove a cyst on his right knee.
Martino said on Friday: "Puyol's return means we have the centre-back we all wanted. I'm very happy about it. The captain is back.
"He is at the end of his recovery. He could be back in full training ahead of next week's game against Real Sociedad."
Barcelona play Sevilla at Camp Nou on Saturday and Martino will be hoping Argentine star Lionel Messi can continue his excellent form.
Messi – who has scored five goals in his two La Liga outings this season – netted a double for Argentina in a 5-2 World Cup qualifying win over Paraguay on Wednesday.
Reports have suggested Martino has asked the Argentina Football Association to refrain from selecting Messi for the country's final two qualifiers, with their position at next year's World Cup already secure.
But the former Paraguay manager refuted those claims strongly.
"We didn't ask the Argentina Football Federation not to call up Messi next time," he added.
"I wouldn't do anything like that, I've been a national team coach myself.
"It's been a while now that Messi has been as good for Argentina as he is for Barca. He's decisive for us and for them."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.