The short answer is "no" - you can buy a single share of any publicly traded company if you want to. Thus, if you have a small amount of money to invest, you can, in fact, buy a small number of shares of a public company. Many brokers will process a trade for a few shares of common stock, as they receive a commission for their services anyway.
However, just because you can invest your savings this way, does not mean that such an investment will be a good one. You have two major obstacles that must be mitigated before going ahead and buying a small number of common shares: diversification and transaction costs.
First, you need to strongly consider the costs of under-diversification if you are going to begin your investment portfolio with a single stock. If you have no other investments, investing in only one company exposes you to an excessive amount of company-specific risk (i.e. if your chosen company is the next Enron, you could lose virtually everything). Thus, if you have a small amount of money to invest, a much more efficient portfolio can be constructed by buying into a mutual fund. A mutual fund is essentially a large basket of investments bundled together, and will provide growth opportunities for a reasonably low amount of risk. (For further reading, see The Importance Of Diversification and Portfolio Protection In Diversification And Discipline.)
Second, even if you can stomach the risks of under-diversification, your next hurdle is a high one: transaction costs. Suppose your brokerage charges you $30 commissions for each trade. If you plan to buy and (hopefully) sell a stock for a profit, you will incur $60 of transaction costs. If you only had $200 to invest, your investment would need to gain 30% ($60/$200) simply to break even - an extremely inefficient investment. Conversely, if you invested the same $200 in an open-ended mutual fund, you would likely only be charged a small management fee of, for example, 3%. This would leave you with 27% of the 30% you would have had to spend on a single stock purchase. (To learn more, see Don't Let Brokerage Fees Undermine Your Returns.)
When combined, transaction costs and the risk of under-diversification usually prove to be too costly for those who only have a small amount of money to invest. Therefore, rather than purchasing a few shares of a public company, buying mutual funds is often a much better option.
Dan Stewart, CFA®
Revere Asset Management, Dallas, TX
In today's world of online discount brokerage firms, buying as little as one share is more feasible, but the trade would still cost around $8 in fees. If you choose this approach, stick with the best, strongest companies in the world. You could first buy a couple of shares of a high-tech stock, say, and then next time buy shares of an industrial or consumer stock so that you aren't concentrated within one sector. Your portfolio will be more volatile, but you could easily make more money in the long run.
Alternatively, you could invest in an ETF or a conventional mutual fund and get immediate diversification with one trade. Mutual funds typically have minimums of $500 to $3,000 initially, but then you can add in $500 dollar increments. If it’s for an IRA, the minimums are usually lower.