Jerry Brown ordered "all necessary and viable actions" be taken to stop it.
More than 2,000 families have been moved from their homes and many people have reported feeling ill because of the leakage, which began in October.
It stems from a vast underground storage field in Porter Ranch, on the outskirts of Los Angeles.
Gas is spewing into the atmosphere at a rate so fast that the well now accounts for about a quarter of the state's total emissions of methane - an extremely potent greenhouse gas.
The well is situated in a mountainous area more than a mile away from residential areas, but residents have complained of health effects like headaches, nausea, vomiting and trouble breathing.
"Let's call it an environmental and public health catastrophe," Tim O'Connor, a lawyer with the Environmental Defense Fund, told the BBC's environment correspondent, Matt McGrath.
"In terms of timelines this is going to surpass the gulf oil problem by a mile. What we do know is that that climate equivalent of this leak is like burning thus far almost 700 million gallons of gasoline or it's the same amount of pollution as 4.5 million cars put out every day, it's tragic."
Methane - the main component of natural gas - is a very strong greenhouse gas, capable of trapping solar radiation in the atmosphere.
It belongs to a category of gases called short-lived climate pollutants.
While methane and other short-lived pollutants remain in the atmosphere for a relatively short time compared to other gases, the California Air Resources Board says that "when measured in terms of how they heat the atmosphere, their impacts can be tens, hundreds, or even thousands of times greater than that of carbon dioxide".
The BBC's Matt McGrath says the large amounts of powerful gas that are leaking could have a significant impact on climate change.
Residents have been complaining of nausea, headaches and other symptoms, but the utility company says that "scientists agree natural gas is not toxic and that its odorant is harmless at the minute levels at which it is added to natural gas".
Health officials in the area have said the long-term effects of being exposed to the gas are unknown.
The utility company is providing temporary accommodation or funds for the displaced residents, and several thousand people in Porter Ranch have been relocated while the gas continues to leak and repairs take place.
But, according to CBS News, only 2,200 families have been relocated even though 6,500 have applied for help.
"You have kids going to school outside their neighbourhoods, families that are living in hotels" says Paula Cracium, president of the Porter Ranch Neighborhood Council. "The longer this goes on the more stress there is."
A broken injection-well pipe about 500 ft (152.4m) below the surface is believed to be the culprit behind the leak, reports say. Pipes like this are used by utility companies to insert gas into the ground for storage until a later time when it can be withdrawn and sold for use.
It is not known why the pipe ruptured.
The facility, a depleted oil field, was acquired by Southern California Gas Company (SoCal Gas) decades ago for use as a natural storage facility for gas piped in from as far away as Canada, according to the Los Angeles Times.
Using former oil fields as storage for natural gas is quite common in the US. The US Energy Information Administration says that "most existing natural gas storage in the United States is in depleted natural gas or oil fields that are close to consumption centers," like the large metropolitan Los Angeles area.
Repair work has been slow due to the nature of the leak.
SoCal Gas has tried to plug the leak on several occasions, according to the LA Times. Their first attempt was foiled by ice formations that prevented a cocktail of chemicals and mud from reaching the leak point. Another seven attempts failed because the upwards pressure of the leaking gas was greater than the pressure that they could use to push the mud-chemical cocktail into the earth.
Engineers then began to worry that if they applied any more pressure, they may damage the pipes further and worsen the leak.
The new plan is to drill two new "relief wells" that would use less-obstructed and bigger piping to insert the mud-chemical cocktail into the system far below the point at which the pipe is believed to have ruptured. But the company says that this plan could take months and would not be completed until February or March.
In the meantime, the company is installing large mesh screens around the leak site to try and hinder the oily mist from spraying down on the community.
"The stain of this disaster is going to be felt for quite some time," Ms Cracium says.
The governor of California has declared a state of emergency in a suburb of Los Angeles over the leaking of methane gas from an underground storage field.