The First Amendment clearly does protect businesses in some ways. However, it is not generally correct to say that it limits business. Instead, we can say that there are ways in which the First Amendment fails to protect business.
The First Amendment protects business in at least two major ways. First, the amendment has been construed to allow businesses to engage in political speech. This means that businesses can advocate for issues that are important to their success. Second, and perhaps more importantly, the amendment protects advertising as part of freedom of speech. The government can generally not prohibit advertising unless it has a substantial interest in doing so and unless the governmental regulation is as limited as it can be.
However, the First Amendment does not protect businesses in some other ways. For example, there are times when the government is allowed to regulate advertising. One way it does so is by prohibiting certain kinds of advertising of cigarettes and of liquor. The amendment also does not protect businesses if they engage in misleading advertising.
Thus, the First Amendment protects businesses in some ways, but fails to do so in others.