The resignation follows an investigation by the EU's anti-corruption agency OLAF. Dalli, from Malta, claims his innocence.
The Swedish firm says it was offered influence that would lead to looser EU rules on snus in exchange for cash, and the European Commission claims the man that made the offer had links to Dalli.
Snus is moist tobacco that is placed under the upper lip and is popular in Sweden, but banned under EU rules in the rest of the continent. Swedish Match and the Swedish government have been campaigning for more relaxed rules.
Swedish conservative Moderate Party MEP Christofer Fjellner told Swedish Radio News:
"If corruption has reached the very top of the EU, it makes me terrified. It's a good example of moral courage that this Swedish company decided to report the attempt, rather than follow into the mire of corruption."