Hansi Flick's side have started the season with a perfect record after five La Liga matches but struggled to find their best level against the Ligue 1 side.
Paris Saint-Germain were confirmed as Ligue 1 champions on Sunday without playing after closest challengers Monaco lost 3-2 away to Lyon.
"Monaco are a team on the same level as us and also aspire to win the league, so it is a good result," said PSG coach Luis Enrique
Messi played the full 90 minutes of PSG's 2-1 defeat by Olympique Marseille in the French Cup on Wednesday and the 35-year-old is in a race against time to be fit for their Champions League last-16 clash with Bayern Munich on Tuesday.
French champions Monaco finished the Ligue 1 season in style with a record 12th consecutive win as they beat Stade Rennais 3-2 away on Saturday.
For Monaco, after the euphoria of a league title won in brilliant style will come the realisation that this could be the start of a glorious era.
Teenage star Kylian Mbappe helps Monaco secure their first Ligue 1 title in 17 years with his 15th goal of the season in Wednesday's 2-0 victory at home to Saint-Etienne.
A stunning Dani Alves volley helped Juventus stroll into their second Champions League final in three years on Tuesday, a 2-1 win on the night completing a 4-1 aggregate victory over outclassed Monaco.
Monaco edge closer to a first Ligue 1 title since 2000 as a 3-0 win at Nancy gives them a three-point lead over defending champions Paris St Germain.
Holders Paris St Germain reached the French Cup final with a thumping 5-0 home win against a weakened Monaco side in a one-sided last-four clash on Wednesday.
A brilliant Monaco side that has taken Europe by storm will not relent in their bid for glory after beating Borussia Dortmund to reach the Champions League semifinals, promised coach Leonardo Jardim.
Borussia Dortmund, still shocked after a bomb attack on the team bus last week, have a slim chance of overturning the 3-2 home loss to Monaco in their Champions League quarterfinal first leg, club CEO Hans-Joachim Watzke says.
Radamel Falcao struck a superb winner as Ligue 1 leaders Monaco came from behind to beat Dijon 2-1 at home on Saturday, while Nice remain firmly in the title hunt after downing Nancy 3-1 to guarantee a top-three finish.
Tiemoue Bakayoko's superb header fired Monaco into the Champions League quarter-finals as Wednesday's 3-1 victory condemned Pep Guardiola's Manchester City to a painful exit on away goals.
Monaco owe most of their recent success to their young guns, but when they face Manchester City looking to overturn a two-goal deficit in their Champions League last-16 tie on Wednesday, they will turn to a more experienced player in Radamel Falcao.
Sergio Aguero stars as Manchester City beat Monaco 5-3 in a breathless and dizzyingly end-to-end Champions League last-16 first-leg encounter at a rocking Etihad Stadium.
Mario Balotelli and Younes Belhanda were sent off in the dying seconds as Ligue 1 leaders Nice stumbled into the winter break with 0-0 draw at Bordeaux, allowing Monaco to trim the gap at the top to two points.
Defending champions Paris Saint-Germain eased into the French League Cup quarter-finals on Wednesday with a 3-1 win over Lille while Monaco routed Rennes 7-0.
Tottenham Hotspur manager Mauricio Pochettino admits his side have struggled to cope with the twin demands of playing in the Premier League and in Europe after their shock exit from the Champions League.
