Capitalism could be compatible with Islam, just as it could be compatible with other religions such as Christianity and Judaism. But whether it will work or not is up to the culture that adopts and adapts it. There is nothing inherently Muslim that would preclude the following of capitalism as economic policy.
Islam tends that everyone is equal without any discrimination or something. In this way the government acts firmly thinking equally about everyone. Also it doesn't spend resources for nothing. In Islam everything has it golden value and nothing can change that. A religions that tends the best for the human kind and a person who is muslim knows best how to deal with different problems that the government has to.
The two are different concepts that can be compatible. Islam is a religion. Capitalism is a system in which resources are to be allocated to be private contractors. Islam has worked with capitalism in many countries. For example, Saudi Arabia, Kuwait, Bahrain. There are many more. In fact some of the countries I mentioned are flourishing economically compared to many countries that are predominantly Christian.
Why is this even a question? There are so many examples of Islam rejecting capitalism and even democracy. In fact, when Islam had the choice to elect their first freely elected leader in Egypt, they chose a religious radical who plunged the country back into authoritarianism again. I am beginning to believe that the only way that Islam will become tolerant is when it is gone.