More than 260 children had been left at the welfare home in Guangzhou since 28 January, director Xu Jiu added.
Staff will continue caring for babies already at the welfare home, all of whom suffer from illnesses, Mr Xu said.
China introduced the centres so parents could abandon infants safely rather than leaving them in the streets.
Supporters say the baby hatches save lives, but critics say they encourage parents to abandon their children.
Mr Xu announced the suspension on Sunday, saying that 262 babies had been left at the centre since the scheme began in January.
"I hope everyone understands the difficulties the welfare centre faces," Mr Xu told Xinhua news agency.
"We are temporarily closing the centre [to new babies] so that we can properly care for the infants already at the centre."
The centre, which also cares for orphans, has 1,000 beds.
However, it currently houses 1,121 babies and young people, with another 1,274 in the care of foster families, Guangzhou's Municipal Civil Affairs Bureau said.
All the abandoned infants had illnesses, such as cerebral palsy, Down's syndrome and congenital heart disease, the bureau added.
It is thought that many parents abandon ill babies because they fear they cannot afford the medical care required.
Abandoning children is illegal in China. However, authorities believe that the hatches give the infants a better chance of survival than if they were left in the street.
A total of 25 baby hatches have been established in 10 provincial regions in China, Xinhua reports.
Under China's strict population control policies, most couples have only been allowed to have one child and there is a strong preference for healthy baby boys.
In December, China's top legislature formally adopted a resolution easing the one-child policy, allowing couples to have two children if either parent is an only child.
Provinces are now determining when to relax their restrictions at a local level, with some acting already.
A baby hatch in southern China has been forced to suspend work after hundreds of infants were abandoned, overwhelming the centre, its director says.