The 21-year-old is likely to play in Thursday's third qualifying round tie, with Chico Flores still recovering from a thigh injury, and Amat feels it is a fixture that represents a personal milestone.
It would be his first competitive fixture for Michael Laudrup's side after joining from Espanyol and the Spaniard is keen to play a part.
"Facing Malmo will be the biggest game of my career so far," he told the club's official website.
"The Europa League is a big competition and this game is very important."
Amat is likely to be paired with Ashley Williams at the centre of Swansea's defence against Malmo, who finished third in last season's Allsvenskan.
The Spain Under-21 international is focussed on keeping Rikard Norling's strikeforce quiet.
"Malmo won 7-0 (against Scottish side Hibernian) last week, so it’s important for us to keep them at zero," Amat continued.
"It’s very good to play alongside Ashley. He’s a very good player and easy to play with.
"He speaks a bit of Spanish and that has helped me. It’s made my life much more easier.
"We have a lot of Spanish players and the relationship is very good. Everyone at the club gets on well together."
Amat played the full 90 minutes in Swansea's 3-0 friendly win over Reading on Saturday as the Welsh side maintained their 100 per cent pre-season record.
