Tang Yong Jian, 40, pleaded guilty to charges of illegal possession and dealing in ivory, after he was arrested last week while on transit from Mozambique to China via Nairobi.
He was carrying a small elephant ivory tusk weighing 3.4 kilogrammes (7.5 pounds) in a suitcase.
Under the new law, dealing in wildlife trophies carries a fine of not less than Sh1mn or a minimum jail sentence of five years, or both.
Tang is due to be sentenced on Tuesday.
The most serious wildlife crimes – the killing of endangered animals – now carry penalties of life imprisonment, as well as fines of up to Sh20 million.
For years, Kenyan courts had their hands tied by laws that limited punishments for such crimes, but a new wildlife act signed into law this month has provided far stiffer penalties.
Previously, punishment for the most serious wildlife crimes was capped at a maximum fine of Sh40,000 and a possible jail term of up to 10 years.
Some smugglers caught in Kenya with a haul of ivory were even fined less than a dollar apiece.
Kenya is a key transit point for ivory smuggled from across the region.
Poaching has risen sharply in Africa in recent years, with rhinos and elephants particularly hard-hit.
Asian consumers who buy smuggled rhino horn – which is made of keratin, the same material as human fingernails – believe that it has powerful healing properties.