Any time you analyse a human system based on material conditions and economic class as organizing factors you are doing Marxist analysis.

Please explain what is meant by "early modern." There are Marxist critiques and analysis giong on everywhere. My favorites include Gramsci, Wallerstein, and of course Braudel discusses the emergence of capitalism.

Well, I think we use Marxist theory in many ways, but we don't necessarily rely on him in the same way we did in the past. Obviously people still study him and he still informs our thoughts if not directly than indirectly--theorists like Jurgen Habermas are heavily influenced by Marxism, and even those who build their theories in disagreement with Marxist analyses are in their own way still relying on Marx. Early Modernists definitely have this specter of "pre-capitalism" or "early capitalism" looming over them at all times because even if capitalism isn't literally the root of all historic change, it is incredibly important and there's still much more to be said about its origins and affects. In some ways we owe the transparency of capitalism to Marx, and thus the question of its origins is inherently a Marxist question.

He's definitely not gone completely, and he may even be making a comeback. In Spring 2014 William Sewell from U Chicago published an article called "Connecting Capitalism to the French Revolution: The Parisian Promenade and the Origins of Civic Equality in Eighteenth-Century France" in which he adopts a Marxist analysis of 18th Century France and the French Revolution. This is significant because there had been a predominant Marxist approach to the Revolution for quite some time, but, as Sewell writes, "...since the 1960s, this Marxist or Marxisant explanation has been thoroughly undermined by historical scholarship. Above all, it turned out to be impossible to find any coherent “revolutionary bourgeoisie” that seized power in 1789." The French Revolution is a hot topic for revisionist history, perhaps the hottest, and so to return to a model that so many people have spent so long utterly dismantling seems a bit odd. He takes a different approach and argues that capitalism results in the diffusion of commodity exchange, an economic model which brings with it a broader social participation in relationships that are inherently abstracting: you're exchanging items that have both a concrete use value and an abstract exchange value, and because the relationships you're building between yourself and others are based on this navigation of the abstract, your place in that market is therefore abstract. He extrapolates that this economy and the conditions it produced--the blurring of social distinctions and the new spaces free from traditional dictum--all combined to make a society organized by abstract notions of civic equality thinkable to the French, and therefore the Revolution was possible.

He actually makes a pretty solid argument, even though I disagree with him and I think there are some parts of the argument that need more support. Either way, it's very cool to see someone approach the subject from this angle and I really hope to see more. Actually it's interesting that you asked this question. Perhaps it says something about this post-cultural-turn that we may or may not be in and the renewed interest in older models with new perspective, as Sewell has done.

A much more extensive answer of mine for a very similar question a little while ago. By way of summary, yes, Marx is a very influential in the social sciences, even of periods before the development of full-fledged capitalism. While his perceptive explanation of the capitalist system is still relevant, and most useful for history of the last two to three centuries or so, he has a particular perspective that has been often copied. In both archaeology and history, the "history from below" approach, where you look at commoners and other people outside positions of social power and prestige, was in large part inspired by Marxian thought.

Likewise, world-systems theory as others have also mentioned. Post-colonial theory, as a wide body of work, has also been heavily inspired by Marx.

Finally, archaeologists have in many ways taken Marx to heart, directly or not, because his focus on production and the material conditions of human life correspond really well with archaeological data which is, by definition, material. Probably the best kind of information archaeology can provide on any past society is how they organized themselves economically, and so Marx's supposition that that economic organization influences many other aspects of society is very appealing to archaeologists who otherwise have a hard time accessing those parts of society (such as religion or other kinds of ideology).