Yes, absolutely. For a system to be capitalistic, you also have to have at least capital intensive means of production (hence the name), a real labor market and more or less free access to the market both as a consumer and a producer. Capitalism only started existing with the onset of the industrial revolution.

Reductio at absurdum: A Greek citizen in 200 BC is buying fish from a fisherman, with coins, at freely decided prices. Thats the market at work, but no capitalism at all.

You could imagine (as a quick, not particularly explored example) a society where there's only a market for labour, and the state leases all durable goods, and sells or provides all consumables.