Mrs Key had to put on protective garments and gloves before she got to hold the baby for five minutes.
Then Xing Yu was taken back to her room, where she apparently sleeps for 20 hours a day.
Before the Keys' arrival in Chengdu, in western China, the PM told reporters it would be great for a New Zealand zoo to get a couple of pandas but there was a lot of international demand and a huge queue.
They also cost about $1 million each.
"But the real issue isn't the cost. It is whether we can actually get access to them," he said.
"If we really called in a favour, I'm sure we could move ourselves up the queue, but we have probably got bigger fish to fry in China than that."
Mr Key opened New Zealand's fourth diplomatic post in China at Chengdu, in Sichuan province. He was accompanied by a New Zealand business delegation, most of whom already do business in the people's republic. The consulate will have up to six staff.
After visiting Chengdu, Mr Key left for the East Asia Summit today in Burma, the country's biggest undertaking since emerging from 50 years of military rule.
The event is a summit of the 10 Asean countries and eight others -- the United States, China, Russia, Japan, India, South Korea, Australia and New Zealand.
Mr Key first visited Burma in November 2012, one of the first Western leaders to do so in recognition of its move towards democracy.
By Audrey Young of the New Zealand Herald in Chengdu
