During the first part of 2015–16 season, Sadiku was used scarcely, and often as a substitute by coach Sami Hyypiä despite being the team's top goalscorer in the league. That lead him to request a loan to another Swiss Super League side in order to play more to be ready to represent Albania in the UEFA Euro 2016 in France. His wish was fulfilled and on 12 January 2016 Sadiku was loaned out to the bottom-side Vaduz until the end of season. During his presentation one day later, Sadiku was allocated squad number 32 and dubbed his Vaduz move as the "right decision". His parent club Zürich was criticized by the Swiss media, which dubbed the loan an "own goal" and an "arrogant" decision.
On 21 May 2016, Sadiku was named in Albania's preliminary 27-man squad for UEFA Euro 2016, and in Albania's final 23-man UEFA Euro 2016 squad on 31 May. He made his first ever UEFA European Championship appearance on 11 June 2016 in the opening Group A match against Switzerland as Albania conceded early and lost 0–1. In the final group match versus Romania eight days later, Sadiku netted a header in the first half to lead the team to a historic 1–0 win; in doing so, he became the first Albanian player to score a goal in the UEFA European Championship and Albania took their first ever win in a major football tournament. It was also Albania's first win over Romania since 1948. Albania finished the group in the third position with three points and with a goal difference –2, and was ranked last in the third-placed teams, which eventually eliminated them.
For the qualifiers of 2018 FIFA World Cup qualification, Sadiku's Albania was placed in Group G along with Spain, Italy, Israel, Macedonia and Liechtenstein. On 29 August 2016, he was in the team's for the friendly against Morocco and the opening qualifying match against Macedonia. He played as a second-half substitute in team's goalless draw against Morocco at the newly renovated Loro Boriçi Stadium. On 5 September in the match against Macedonia, Sadiku opened the score with right-footed shoot just outside the box as Albania won 2–1 thanks to a goal in the last minutes. Later that month, Sadiku suffered an injury while playing for Zürich which kept him sidelined for the next two qualifying match against Liechtenstein and Spain in October, which ended respectively with a 2–0 win and 0–2 defeat. He also missed the match at Elbasan Arena against Israel which ended in a 0–3 defeat as Albania was dropped to fourth place.
In April 2016, Sadiku signed a sponsorship deal with American sportswear and equipment supplier, Nike.