You’ll generally face two minimums: A brokerage account minimum, which typically falls between $0 and $2,500, and the mutual fund minimum, which may be $1,000 or more. These minimums are combined — if the broker allows you to fund an account with $1,000, you can then invest that money in a mutual fund with a minimum of $1,000. As referenced above, many brokers now offer mutual funds with no or low minimums.
If your broker doesn’t, you might consider exchange-traded funds, which are a type of passive mutual fund you can buy for a share price, much like an individual stock. That often means a lower barrier to entry. (Compare mutual funds vs. ETFs.)