Chris Coleman's team are likely to face a tough draw as they will be one of the lowest-seeded teams.
But former striker Rush believes the biggest nations will not want to face a Welsh side which lost only once in qualifying.
"They won't want Wales in their group," Rush told BBC Wales' Sport Wales.
"I'm not saying we are going to win it but the opposition won't like to play Wales.
"Every game will be a big test and they will learn from it and I think we will win a game."
Rush is the country's all-time leading goalscorer with 28 goals, while Gareth Bale took his tally to 19 with Wales' second goal in the 2-0 win over Andorra.
Real Madrid forward Bale scored seven of Wales' 11 goals in Euro 2016 qualifying, with Aaron Ramsey netting twice and Hal Robson-Kanu and David Cotterill scoring one apiece.
But former Liverpool and Juventus striker Rush is not too concerned by Wales' limited forward options.
"The lads that play there I think you forget the work that they do. They put in a tremendous work rate," Rush added.
"What we may be missing is someone to tap the ball in
"But Robson-Kanu, [Sam] Vokes and [Simon] Church give it 110% so you can't knock that. I think sometimes you need that goal to give you confidence.
"Get the confidence in the friendly internationals and you never know what might happen."
*Watch Sport Wales most Fridays on BBC Two Wales and for seven days after transmission on iPlayer
Wales should fear no team at the 2016 European Championship finals in France next summer, says all-time leading goal scorer Ian Rush.