Shakib was ruled out of the upcoming three-match one-day international series at the last minute, with a fracture to the little finger on his left hand.
The all-rounder's absence will certainly make winning tougher for Bangladesh, who have not defeated New Zealand in any format during their previous four tours to the country.
Bangladesh’s only win in New Zealand came in 2015 when they beat Scotland by six wickets in a World Cup group match at Nelson.
"It was already a big challenge. The loss of Shakib made it a bigger challenge," Mashrafe told reporters before leaving for New Zealand on Sunday.
"We have to play with a positive frame of mind," he said.
Mashrafe did not rule out the possibility of winning the series against New Zealand, despite their poor record in the country.
"Mental strength" is crucial, he said, for his team to pull off a surprise win.
The final stage of the Bangladesh Premier League also bolstered Mashrafe's hopes for success, as he watched some of the team's batsmen return to form.
Opener Tamim Iqbal struck a magnificent 141 off 61 balls in the final of the tournament to power his Comilla Victorians beat Shakib’s Dhaka Dynamites by 17 runs for the title.
"The kind of wicket we got in the BPL semi-final and final – I think the wicket (in New Zealand) will be similar and flat," Mashrafe said.
"It’s a relief for us that the batsmen returned to form. The challenge is now for the bowlers."
Bangladesh will play three Test matches, along with the ODIs, during their long visit to the country. The first Test is due to start on February 28 in Hamilton.