The Brazilian, who joined the Liga champions from Santos for €57 million [£48m] this summer, was diagnosed with a low red blood cell count - which can cause excessive levels of tiredness in players - following routine blood tests.
But Zubizarreta has insisted the 21-year-old's condition, which comes a month after the attacker had his tonsils removed, is something the club will manage and is not overly serious.
"We would have liked him to have been in perfect condition, but not many players arrive perfect for the pre-season," Zubizarreta said.
"We'll help make sure he's in the right condition. It's not a concern.
"There are quite a few days left before the league starts, although it is unlikely that he'll be 100 per cent adapted [to Barcelona's style] by then.
"But we can clearly see that he's quickly getting a grasp of our type of football."
Neymar made his Barcelona debut in a 2-2 friendly draw against Lechia Gdansk on Tuesday before appearing off the bench in an 8-0 win over Santos on Friday.
Barcelona begin the defence of their Spanish top flight title with a home fixture against Levante on August 18.