If there is a single thesis statement in the Communist Manifesto, it is this, found in the introduction to the document:

[N]ot only has the bourgeoisie forged the weapons that bring death to itself; it has also called into existence the men who are to wield those weapons — the modern working class — the proletarians.

This statement sums up the core arguments of the Manifesto: history is properly understood in terms of class relations based on economic terms; conflict between social classes advances history; industrial development has created the bourgeoisie and the proletariat; and history is moving inevitably toward the destruction of the former by the latter.

The context for the Manifesto was the revolutions that convulsed Europe in 1848—revolutions which Marx and Engels saw as harbingers of the open class confrontation that would destroy the bourgeoisie. By this point, the authors argued, the bourgeoisie had become so powerful and had so thoroughly ripped apart the traditional forces that bound society that a cataclysm was near.

To put it another way, only by increasing exploitation of the proletarian working class could the bourgeoisie survive. The more the working class was exploited, however, the more restive it would become, and the more alienated it would be from the fruits (the economic value) of its labor. In other words, the more successful the bourgeoisie was, the more dangerous and disaffected—not to mention numerically stronger—the proletariat would become. The fact that the proletariats would be increasingly crowded into factories, instead of piecemeal across farms and workshops, would make them easier to organize and more likely to understand their own class interest.

In this way, as the Manifesto argued, the bourgeoisie's expansion and success paved the way for its inevitable destruction. There are many memorable passages in this extraordinary document, but this one encapsulates its thesis.

To create a thesis statement for The Communist Manifesto, first take a look at the Preamble or the introduction in which Marx and Engels outline one of the central ideas of this book. In this section, they argue that communism is a "spectre" which haunts Europe. In other words, communism already exists and it is ready to come to the fore of European politics.

Secondly, take a look at the first chapter of the book in which Marx and Engels argue that all history is the history of class struggles. Specifically, they show that society has split into two groups: the proletariat and the bourgeoisie. It is this second group, the bourgeoisie, who have come to control society through their exploitation of the proletariat and their labor.

Putting these two arguments together, then, we can formulate the following thesis statement: The proletariat is exploited by the bourgeoisie and communism provides the only realistic solution to this problem.

There could be a number of things that would serve as a thesis statement for this work.  I will identify two of them here.

First, there is the beginning of the work.  It reads

The history of all hitherto existing society is the history of class struggles.

This can be seen as the thesis of the work because it gives the Marxist view of all of history.  Marx believed that all of human history was a story of classes in conflict with another.  This would continue until communism was finally established.

A second possibility comes at the end of the first chapter of the work.  There, Marx says that

What the bourgeoisie therefore produces, above all, are its own grave-diggers. Its fall and the victory of the proletariat are equally inevitable.

We can say that this is the thesis statement because it gives the most relevant idea of the book for our own time.  Capitalism is the system that exists in our own time and we are interested in what will happen to it.  According to Marx, it will fall and the proletariat will rise, eventually creating communism.

You can make an argument for either of these being the thesis of the work.