That's the question posed by Benedikt Koehler. Capitalism, he asserts, first emerged in Arabia, not in Europe as is commonly assumed. Islamic institutions and business practices were adopted and adapted in Venice and Genoa. These financial innovations include the invention of the corporation, business management techniques, commercial arithmetic, and monetary reform. There were other Islamic institutions assimilated in Europe: charities, the waqf, inspired trusts, and institutions of higher learning, the madrasas, were models for the oldest colleges of Oxford and Cambridge. As such, it can be rightfully said that these essential aspects of capitalist thought all have Islamic antecedents.
I wouldn't call the Prophet ﷺ a capitalist. Once you're a Prophet, you don't need another label. But names and terms are a side point. Islam brings forth its own unique economic system neither capitalist nor socialist. It will have features people say is capitalistic, and others which people will say is socialist, etc. Overall, the laws tend to be capitalistic, while the attitudes are socialistic. Here are eleven basic principles...
1 The Prophet ﷺ set up a market for the people, not controlled by the state.
2 He ﷺ did not tax it.
3 He ﷺ "was going to set prices, but determined that prices are in the hands of Allah."
4 People can own wealth, land, & the means of production.
5 The ruler has no rights over people's wealth (this hugely limits the ability to levy taxes).
6 The primary concern of the ruler, as per Sayyidna Umar, is "the stomachs of the poor."
7 Wealth sitting idle for a year is to be given to the poor at a rate of 2.5%.
8 Money-lending is an unlawful industry when the loan results in an increased return for the lender.
9 Finance requires partnership.
10 Wealth is better from the aspect of helping others: advancing the deen, supporting the needy, not having to ask people for money.
11 Poverty is better for one's own individual soul, based on the hadith, "You will conquer Persian & Byzantium and have one dress for the morning and another one in the evening."
"Will we be better off at that time?"
"No, you are better off now."