Both classical and marxian schools assume the (cultivated) land to be means of production. The differentiation between land and shovel for example is that the land is considered natural resource (subject of labor) while the shovel is an instrument of labor.
Subjects + instruments together = means of production.
Owning the means of production is a necessary but not sufficient factor for a capitalist to exist. There is an umbrella of conditions and pre-conditions (i.e. ownership of labor-power, ownership of capital, capitalistic mode of production in society, advanced credit/banking system etc. ) that need to occur.
For example, big land owners in Medieval times were feudal lords but not capitalists, since capitalistic mode hadn't emerged yet. A small peasant who owns a small piece of land and uses it to feed his family nowadays or sells some part of the crops in the local market, is not a capitalist, since he lacks capital and doesn't have ownership of other labor but his own.
PS. That was the analysis for the question, bearing in mind that we are talking about land used for farming. Using it for other purposes (ex. rent) needs a more elaborate analysis.