Defeat leaves Arsenal in sixth place, five points off the top four and without a win in five games in all competitions.
French League Cup: Neymar, Adrien Rabiot on target as Paris Saint-Germain beat Amiens to reach semi-finals
Neymar scored a penalty as four-time defending champions Paris Saint-Germain beat 10-man Amiens 2-0 to reach the semi-finals of the French League Cup.
Lemar, who has been heavily linked with a move to England, nodded Monaco into an early lead.
January transfer window: Barcelona snap up Philippe Coutinho from Liverpool in whopping €160 million deal
The swoop for the 25-year-old Coutinho — which contains a 400 million euro release clause — will be the third biggest deal in football after those for Neymar and Kylian Mbappe.
Coutinho's departure would be a blow to Liverpool, but it would allow Barcelona to move on from losing his Neymar to Paris Saint-Germain last summer.
Premier League: Arsenal manger Arsene Wenger says club open for any 'exceptional player' who can add value
Wenger, whose transfer dealings have been a sore point with sections of the Arsenal support, said he would also be on the look-out for players in the present transfer window.
Wenger says he has no concerns over the commitment of the pair, with Sanchez scoring a last-gasp penalty as the Gunners won 1-0 at Burnley on Sunday.
Ligue 1: Edinson Cavani scores 100th league goal as Paris Saint-Germain thrash Angers; Monaco defeat Guingamp 6-0
A second successive five-goal victory for PSG means they remain unbeaten in all competitions this season, while Angers are still without a home win.
Ligue 1: Monaco win comfortably despite Radamel Falcao's absence; Dijon's Julio Tavares helps beat Nantes
Monaco eased to a 2-0 victory away at Bordeaux in Ligue 1 on Saturday, but Claudio Ranieri's Nantes went down to a rare defeat.
Ligue 1: Keita Balde opens account for Monaco; Nantes mark coach Claudio Ranieri's 66th birthday with win
Keita Balde netted his first goal since his big-money summer move to Monaco as the reigning French champions eased to a welcome 2-0 victory at home to Caen in Ligue 1 on Saturday.
Raheem Sterling said on Monday he sees his long-term future at Premier League leaders Manchester City and has no interest in a move to Arsenal.
Monaco went into the game after a surprising 3-0 Champions League loss at home to Porto in midweek
Tuesday's Champions League action will see holders Real Madrid take on Borussia Dortmund and Pep Guardiola's Manchester City host Shakhtar Donetsk among other matches
Ligue 1: Paris Saint-Germain's Neymar, Kylian Mbappe and Edinson Cavani look to continue goal-scoring run
Paris Saint-Germain and their fearsome attacking trio of Neymar, Kylian Mbappe and Edinson Cavani host Lyon on Sunday looking to make it six successive wins to kick off the Ligue 1 season.
The news means the pair will definitely miss Monaco's match against Strasbourg and the visit to Lille on 22 September.
Just eight years after starting life in the local leagues, RB Leipzig will enhance their rags to riches tale on Wednesday by hosting Monaco on the German club's Champions League debut.
Arsene Wenger also admitted Jack Wilshere could make his long-awaited return to the Arsenal first-team for Thursday's game.
Premier League: Liverpool hope to maintain winning run in clash with Pep Guardiola's Manchester City
Coutinho could make his return to action for Liverpool against Manchester City.
Arsenal manager Arsene Wenger has voiced confidence that Alexis Sanchez will put his aborted transfer to Manchester City behind him 'very quickly' says he is strong mentally and hopefully he will be back very quickly to his best.
Premier League: Arsene Wenger's 21-year-journey with Arsenal could be coming to an unceremonious close
But after a miserable start to the Premier League campaign, Wenger once again appears trapped in a debilitating cycle of on-field underachievement and behind-the-scenes unrest.