The third qualifying round first-leg meeting at the Liberty Stadium will mark the first time Swansea have taken part in continental competition since 1991, when they were thrashed 10-1 on aggregate by star-studded Monaco in the Cup Winners' Cup.
Their appearance in Europe comes courtesy of their Capital One Cup success last season and Laudrup is eager for the Welsh club to savour the experience earned by their Wembley triumph.
"Of course it is special," said the Dane, who was no stranger to success in Europe during his playing career, helping Barcelona win the European Cup for the first time in 1992.
"Suddenly as a player and a manager you are against sides you are not used to facing. In the league you play and you go on and on, here you have two games and one team will go out.
"The only time we tried it last season was the fantastic semi-final against Chelsea in the cup.
"But even with the cups here in the UK it is usually one game, here it is two legs and even in the first game you have to think ahead. It is very different."
He added: "I think this tie is quite even because they are where they are and we are just at the beginning of the season. But I would be disappointed if we didn't go through to the next round.
"I think we have a team that has the quality to go to at least the group stage. But we have to show that in the next eight days against opponents who are match fit.
"When I look at our squad I think we have a team that can disturb a lot of teams out there in Europe, even some big clubs in big leagues.
"Now, we have to play a team who are second right now in the Swedish league and they have that match fitness because of playing so many games. We will be up against it in these two games."
Unlike many of his players, Laudrup has previous experience of the Europa League having guided Getafe to the quarter-finals when the tournament was known as the Uefa Cup during the 2007-08 season.
But Malmo look set to be a tricky proposition for the Swans, having handed a comprehensive 9-0 beating out to Hibernian in the last round.
The Swedish club, beaten European Cup finalists in 1979, also have the advantage of being 17 games into their Allsvenskan campaign which started in April and sit second in the table, while Swansea are still rounding off their Premier League preparations.
But Laudrup is confident his side have the quality and the fitness to handle the visitors, but has stressed the importance of not conceding on home soil.
- Sports & Recreation