The President of the French Football Federation also added that all football league seasons are over, raising questions over which teams will head to the Champions League.
Professional football, rugby and other sports in France cannot resume until the end of the summer because of coronavirus restrictions, Prime Minister Edouard Philippe said on Tuesday.
The announcement was made as the government unveiled its plans to gradually end the lockdown in France from May 11.
The move makes the completion of the 2019-2020 Ligue 1 and Ligue 2 football seasons and Top 14 rugby union campaign appear increasingly unlikely.
However, France's sports ministry told AFP after the speech that sports fixtures could not take place even behind closed doors before the end of July, leaving open the possibility that some matches could still be played in August.
In an address to the National Assembly, Philippe said: "The 2019-2020 professional sports leagues, notably football, cannot yet restart."
"I would like to be precise here, no large sports gathering or any gathering of 5,000 people or more, needing the permission of the local police and long prior arrangements, will be allowed before September," Philippe added.
Ligue 1 had outlined its intention to resume matches in June, with players being recalled to training as of May 11.
The French football league will hold a teleconference on Thursday to decide what to do next.
Season 'definitively over'
Noel Le Graet, the president of the French Football Federation, said that he thinks the Ligue 1 and Ligue 2 seasons are "over".
"We informed the executive board, what it already knew, that Ligue 1 and Ligue 2 will not start, that the National (third tier) will not start or the Women's D1 either," Le Graet told Brittanny-based newspaper Le Telegramme.
"These four competitions are definitively over for the 2019-2020 season."
If the season is abandoned, it begs the question of which teams would qualify for next season's Champions League and Europa League and whether teams would be relegated.
But Lyon president Jean-Michel Aulas, whose side currently sit outside the Champions League places, said he "wasn't sure" the season will be ended.
"Does this mean the championship is over? I'm not sure," he told AFP.
"Since the championship is not finished, I think that it's necessary do everything to find an alternative solution, by playing a certain number of play-offs during the month of August or postponing next season until September 15."
Paris Saint-Germain president Nasser Al-Khelaifi said the Ligue 1 leaders would be prepared to play their remaining games of this season's Champions League abroad.
The French champions reached the quarter-finals with a last-16 victory over Borussia Dortmund behind closed doors shortly before the lockdown.
"We plan on competing in the Champions League, wherever and whenever it is held," he said in a statement.
"If it is not possible to play in France we will play our matches abroad, ensuring the most stringent medical safety conditions for our players and all of our staff."
'At least things are clear'
Le Graet said last week he was hoping both the French Cup and League Cup finals could be played before the league season restarts.
PSG are scheduled to face Lyon in the League Cup final and are then due to play Saint-Etienne in the French Cup final.
French rugby union federation president Bernard Laporte said the announcement gave clubs clarity.
"I thought football would be allowed to restart behind closed doors, but I'm not surprised," Laporte said.
"But its a real headache (because) testing, social distancing, is even tougher in rugby.
"It's clear now anyway, nothing until September."
The Dutch football federation last week became the first in Europe to call an end to its season, with no team declared champions and promotions and relegations scrapped.
The Belgian Pro League is expected to follow suit, although other leagues are still hoping to resume, with the German Bundesliga planning for a possible return in mid-May.
Tour de France set to go ahead
The Tour de France is set to go ahead, though, albeit with restrictions on the number of spectators.
Organisers have already moved cycling's showpiece event from its traditional mid-summer slot and it is now scheduled to start in Nice on August 29.
Around 23,000 people have died so far of coronavirus-linked illnesses in France.
Schools and shops will re-open in May but restaurants and bars will remain closed for now, as will large museums, cinemas, theatres and concert halls.