Obbadi fired home with a powerful 30-metre shot 19 minutes from time as big-spending Monaco, who splashed over 100 million euros (83.18 million pounds) on transfers during the close season, stayed third with 29 points from 14 games.
They trail leaders Paris St Germain, who beat Stade Reims 3-0 on Saturday, by five points while second-placed Lille are on 30 points after Pape Souare's late goal gave them a 1-0 win over 10-man Toulouse earlier on Sunday.
The day was soured, however, by events in the south of France where nine people were injured as St Etienne fans threw seats at home supporters in Nice's Allianz Riviera stadium before kickoff in a game the visitors won 1-0.
Monaco, who had taken only one point from their two previous league outings and lost in the last 32 of the League Cup, were under pressure to keep pace with PSG and Lille.
Obbadi took full advantage of keeper Rudy Riou's poor clearance to give his team all three points in the 71st minute, but they failed to impress, once again.
Radamel Falcao, who has scored nine league goals this season, lost his scoring touch and was substituted shortly after the hour.
Monaco coach Claudio Ranieri told Canal Plus that he had substituted Falcao in order to protect him, claiming the Colombia striker was suffering with a minor injury.
Nantes had a goal disallowed for a foul in the last minute. ($1 = 0.7394 euros)
(Reporting by Julien Pretot; Editing by Toby Davis)
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