More than a third of the city’s bus shelters have been shut for emergency inspections through at least the end of the week after a corroded bolt caused the roof of one on Staten Island to fall earlier this month, officials said.

The shelter operator, JCDecaux, announced the emergency inspections were underway Monday in cooperation with the city’s Department of Transportation.

“DOT expects JCDecaux to keep the city’s bus shelters safe and well maintained,” said DOT spokeswoman Alana Morales. “This matter is concerning and we will hold the contractor accountable for making these fixes expeditiously.”

She added: “We agree with their current actions and will monitor to make sure the shelters are inspected and returned to operation in a safe manner.”

The DOT referred other questions to JCDecaux.

According to details provided by JCDecaux, the emergency inspections are focusing on an older-style installation, which accounts for an estimated 2,500 of the city’s 3,500 shelters.

So far, roughly 1,000 have been examined and inspectors have found problems with approximately 30 of them — or roughly 3 percent, the spokesman said.

The goal is to have the remaining 1,500 inspections done by the end of the week, though repairs could take until the end of the month.

Until then, those shelters are wrapped in yellow caution tape and signs warn riders to stay out.

“This bus shelter has been closed to complete a safety inspection. Please do not stand in the bus shelter,” the notice says. “This bus shelter will be re-opened shortly. Please contact 311 with any questions. We apologize for any inconvenience and thank you for your patience.”

JCDecaux said the affected shelters are evenly spread across all five boroughs, with reports of at least two in Midtown.