Hummler is managing partner of Wegelin, Switzerland's oldest private bank, which is being broken up after it became the target of a Washington clampdown on tax cheats.
Former Swiss lawmaker Franz Steinegger will fill in as chairman of the NZZ board, of which Hummler will remain a member, as he concentrates on dealing with the US authorities.
The ongoing dispute "demands the commitment of both my physical and intellectual capacities," Hummler said in a statement quoted by ATS news agency.
He was elected to the board last year for a four-year term but came under pressure to resign over Wegelin's involvement in the tax evasion affair.
Hummler announced at the end of January the sale of its non-US activities to fellow Swiss bank Raiffeisen as a result of the "increasingly threatening situation" surrounding the 270-year-old Wegelin in the dispute.
Three of its bankers were charged in New York with conspiring to help US clients avoid tax payments at the beginning of the year.
The probe reportedly focuses on 11 Swiss banks, among them Credit Suisse, Switzerland's second largest bank.
Bern is in the process of negotiating a tax agreement with Washington to address the issue of US nationals putting money in Swiss accounts.