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.
The thesis of The Communist Manifesto is encapsulated in the following statement at the end of chapter four:
Let the ruling classes tremble at a Communistic revolution. The proletarians have nothing to lose but their chains. They have a world to win. Workers of the world unite!
The Manifesto understands history as a continuous struggle of the proletarians or workers against the ruling class. It also argues for violent revolution rather than the gradual and peaceful spread of socialism advocated by other groups. Further, this short work is a call to action or a polemic rather than a detailed analysis of the world historical situation found in other works by Marx and Engels.
Both the class struggle and the threat of violence are contained in the statement above: the ruling class and the proletarians are depicted as at odds with one other and the ruling classes are told to "tremble" at the workers. Workers are in "chains" and have a "world to win." These are fighting words. Finally, these words represent the call to action that the manifesto is: workers are rallied to revolution, to shaking off their chains and, finally, are strongly urged to unite.