The port's management said this is helped by an expansion programme.
Kenya is building a $300 million second container terminal at the Mombasa port, the biggest in east Africa, to handle increased trade in the region, driven by a sharp growth in construction, infrastructure development projects and demand for consumer goods from an emerging middle class.
The port also serves neighbouring landlocked nations including Uganda, Rwanda, Burundi and South Sudan, which rely on it for vital shipments such as fuel imports.
A total of 18.639 million tonnes of goods moved through the port in the first 10 months of this year, up from 18.106 million handled in the same period of 2012.
The smooth passage of Kenya's presidential election in March, in contrast with the previous one in 2007 that ended in tribal violence, also helped keep up traffic at the port.
Gichiri Ndua, the port's managing director, said it expected cargo traffic for all of 2013 to rise to just over 22 million tonnes from 21.9 million last year.
Uganda was the dominant transit destination, accounting for 73.1 percent of the cargo, while South Sudan took second place with 11.6 percent.
The East African nation also plans to construct a second port at Lamu, north of Mombasa, with a capacity of 23 million tonnes of cargo per year.