The captain will appear in court on Wednesday on the charge of "operating a vessel in a manner causing unnecessary danger or risk."
If convicted, he faces a maximum fine of $7,800, or up to 12 months imprisonment. New Zealand's oil spill response agency, Maritime New Zealand (MNZ), said it is likely more charges will follow.
The Rena, a Liberian-flagged vessel, struck the Astrolabe Reef, about 12 nautical miles off the city of Tauranga, on the North Island, a week ago.
Hundreds of tonnes of fuel oil have leaked from the ship, leading New Zealand's environment minister, Nick Smith, to call the spill the country's most significant maritime environmental disaster.
MNZ estimates that 200-300 tonnes of oil have leaked from the vessel, which was carrying 1,700 cubic meters (450,000 gallons) of fuel. The agency said a "significant" amount of oil is expected to come ashore within days between the towns of Mount Maunganui and Maketu in the North Island's Bay of Plenty.
Clumps of oil have washed onto Mount Maunganui beach near Tauranga and 53 dead birds have been found and 17 other oil-soaked birds are being treated at a rescue center, MNZ said.
The agency said that about 70 containers had fallen off the ship. Eleven of the ship's containers hold hazardous substances and remain on the Rena. MNZ said it is probable that more containers will fall off due to severe weather conditions and the vessel's heavy list, which has worsened.
Due to the hazard the containers pose to shipping, MNZ said navigational warnings had been issued and major maritime traffic has been re-routed.
Efforts to recover oil from the ship have been a top priority before it can be salvaged, but have been hampered by high winds and strong swells.
Worsening weather prompted the ship's crew to be evacuated as a precautionary measure after a mayday call was made on Tuesday.
MNZ said naval architects are monitoring the vessel and have placed sensors to provide advance warning should the ship's structure come under too much stress, which the agency said is described as being in "relatively good shape."
A rescue center has been set up in Tauranga to clean oil from animals affected by the spill and 15 teams are scouring the coast for oiled wildlife.
Officials fear the stricken ship may spill additional oil as its condition deteriorates.
"I think we'd expect that at some point to have further problems and potentially even break up," Transport Minister Steven Joyce told broadcaster TVNZ.
Greenpeace expressed "extreme concern" about the spill and urged the government to avoid using further toxic dispersants.
"This is an unfortunate illustration of just how difficult it is to deal with oil spills at sea," the organization's Steve Abel said. "Even a slow and relatively accessible oil spill like this one has clearly stretched New Zealand's response capability to its limits.
"It is also a potential disaster for the blue whales and dolphins presently calving in the area, as well as numerous other marine species."