City, the defending Premier League champion, took the top spot in the team vote after beating Liverpool 3-1 on Monday.
Bayer Leverkusen, which beat Borussia Dortmund 2-0 in its season opener in the Bundesliga, was second and Barcelona was third.
Barcelona's victory was the first for coach Luis Enrique in his first league game in charge. And it marked the debut of 18-year-old Munir El Haddadi, who also scored.
Robben scored the decisive goal as Munich began its German league season with a 2-1 victory over Wolfsburg, while Jovetic netted twice for City against Liverpool.
"City won the first star match of the season in the Premier League versus their arch and unexpected rival in 2013-2014," Cedric Rouquette of Eurosport in France said. "All of us noticed that the offensive power and technical abilities of (Manuel) Pellegrini's team will still be there this season."
Leverkusen got a goal after only nine seconds from Karim Bellarabi, and a second-half effort from Stefan Kiessling. Bellarabi's goal is the fastest in the Bundesliga's 52-season history, and he is 10th in this week's poll, while Kiessling is seventh.
Cristiano Ronaldo scored in Real Madrid's 2-0 win over Cordoba on Monday and is sixth, with his side polling eighth.
Tottenham is represented in both the team and player rankings after it began the Premier League season with two wins under new manager Mauricio Pochettino.
The 4-0 rout of Queens Park Rangers on Sunday was particularly impressive, and Pochettino appears to be getting the best out of the players signed after Gareth Bale left the club.
Both Erik Lamela and Nacer Chadli, often criticized in England, have impressed in Tottenham's winning start. Chadli scored twice on Sunday and is eighth in the player vote, while Lamela ended up fifth.
"Erik Lamela's rebirth under Mauricio Pochettino has been an exciting watch so far, with the way he attacks defenders looking more and more like Arjen Robben every match," Sam Tighe of Bleacher report said. "With the ball tied to his left boot on a string, he's perplexing defenders left, right and center."
Atletico Madrid is fifth after beating city rival Real Madrid in the Spanish Super Cup, even though it then began its league title defense with a 0-0 draw at Rayo Vallecano.
Swansea's unbeaten start in the Premier League, including victory over Manchester United at Old Trafford in Louis van Gaal's first game in charge, helped it reach ninth.
AP Global Football 10 rankings
1. Lionel Messi, 110 points.
2. Arjen Robben, 80.
3. Stevan Jovetic, 73.
4. Diego Costa, 58.
5. Erik Lamela, 45.
6. Cristiano Ronaldo, 40.
7. Stefan Kiessling, 39.
8. Nacer Chadli, 38.
9. Munir El Haddadi, 35.
10. Karim Bellarabi, 34.
1. Manchester City, 105 points.
2. Bayer Leverkusen, 98.
3. Barcelona, 87.
4. Tottenham, 76.
5. Atletico Madrid, 64.
6. Bayern Munich, 60.
7. Chelsea, 57.
8. Real Madrid, 46.
9. Swansea, 44.
10. Bordeaux, 33.