The US financial regulator, the Securities and Exchange Commission (SEC), is already suing unnamed traders for insider dealing.
Last Thursday, Heinz was bought for $23bn by Warren Buffett's Berkshire Hathaway fund and 3G Capital.
Unusual trading activity in the shares was noticed the previous day.
"The FBI is aware of trading anomalies the day before Heinz's announcement" a spokesman said. "The FBI is consulting with the SEC to determine if a crime was committed."
The SEC believes that some traders knew about the takeover before it was announced and made $1.7m from the knowledge. It obtained an emergency court order to freeze assets in a Swiss-based account.
The traders in question made risky bets that Heinz's stock price would increase, using financial instruments called options. After the official announcement of the deal Heinz's share price rose by 20%.
"Irregular and highly suspicious options trading immediately in front of a merger or acquisition announcement is a serious red flag that traders may be improperly acting on confidential non-public information" said the SEC's head of the Market Abuse Unit, Daniel Hawke.
There is no implication that Heinz or its new owners have committed any wrongdoing.
The SEC said a bank account at Goldman Sachs was used. Goldman Sachs has said it is co-operating with the investigation.
The Federal Bureau of Investigation (FBI) is joining an investigation into suspicious trades ahead of the Heinz takeover deal last week.