Although Rosický was part of the Dortmund team that reached the final of the 2003 DFB-Ligapokal, losing 4–2 to Hamburger SV, he later described the 2003–04 season as his "worst club season," as Dortmund failed to qualify for the following season's UEFA Champions League competition. He scored his first competitive goal of the 2005–06 season in February 2006, against MSV Duisburg; it was his 16th Bundesliga goal on his 139th league appearance. March 2006 saw him have injury problems with his thigh, but he scored twice in Dortmund's 4–2 win against Hamburg at the end the month. He was linked with a move to Spanish side Atlético Madrid, which he discussed in sports magazine Kicker, although mentioned in March 2006 that he had not signed a contract to move elsewhere.
On 23 May 2006, Arsenal confirmed that they had signed then 25-year-old Rosický on a long-term contract for an undisclosed fee. He made his competitive debut for Arsenal on 8 August 2006 in a 3–0 win over Dinamo Zagreb in a Champions League qualifier. Rosický scored his first Arsenal goal on 13 September 2006 against Hamburg in Arsenal's first Champions League game of the season, which Arsenal won 2–1. On 6 January 2007, he scored twice against Liverpool at Anfield in the FA Cup, in a 3–1 victory for Arsenal. In February 2007, Rosický was announced as the Czech Footballer of the Year for 2006, marking his third time winning the award after previous victories in 2001 and 2002. He scored his first Premier League goal on 11 February 2007 against Wigan Athletic. He also scored against Bolton Wanderers on 14 April 2007 and against Manchester City on 17 April 2007. He finished his debut season at Arsenal having scored six goals in 37 appearances for the club in all competitions.
At the 2006 World Cup, Rosický scored two goals in the Czech Republic's opening match on 12 June 2006 in a 3–0 victory over the United States, the first of which was from 30 yards (27 m) out. He was named as the FIFA Man of the Match for his performance. Rosický played the whole 90 minutes of his country's subsequent matches, against Ghana and Italy, but the Czech Republic lost both games by a 2–0 scoreline and progressed no further in the tournament.
In August 2006, Rosický was made captain of the Czech Republic national side, replacing the retiring Pavel Nedvěd in advance of the UEFA Euro 2008 qualifying process. After a defeat to Germany during the campaign in March 2007, he was among a group of players fined 1 million koruna (£25,000) by the Football Association of the Czech Republic (FAČR) for his part in a party involving prostitutes, for which he later apologised in a press conference. His last appearance of the qualifying campaign was against Slovakia in November 2007. Rosický missed Euro 2008 due to injury, announcing his absence in May 2008. He returned to international football when he started for the Czech Republic on 9 September 2009, in a World Cup qualifier against San Marino, following a 20-month absence due to injury. The game finished 7–0 to the Czech Republic.