A poll next week will choose a new president for the organisation but the ministry says several candidates have questioned Femafoot's screening procedure after being excluded.
Incumbent Mamoutou Toure is currently behind bars, having been held in pre-trial detention since 9 August by the country's anti-graft agency over misappropriation of public funds.
Despite this, Toure is expected to be unchallenged in the presidential race.
In a letter addressed to Fifa's outgoing secretary general, Fatma Samoura, the ministry says it wants to establish a climate of trust in Mali after Femafoot's electoral commission ruled out three candidates: Salaha Baby, Amadou Mahamane Sangho and Sekou Diogo Keita.
Baby has already appealed the decision at the Court of Arbitration for Sport.
"We have received correspondence from several candidates," the ministry wrote to Senegalese Samoura, explaining that those excluded have "identified specific points of violation of the rules" which "are likely to call into question the whole process and make us witness a new crisis in football".
The letter goes on to say that the ministry "cannot accept that the proper functioning of football in Mali is damaged" before warning of "splits in the population between different regions of the country" and even possible "disturbances to public order".
"We ask Fifa to take an interest in the current process so that it takes place in strict compliance with the rules," the letter concludes, asking world football's governing body to act with "real urgency".
The arrest of 66-year-old Toure, who has been Femafoot president since August 2019, has cast doubts over the upcoming elections for new executives.
A member of Fifa's powerful executive council, the corruption allegation against Toure centres around his time as administrative and financial director of Mali's national assembly between 2013 and 2019, before he took charge of Femafoot.
Also currently in custody on charges of offences against public property, forgery and complicity are Femafoot's general secretary Modibo Sidibe and Issiaka Sidibe, a former president of Mali Premier League club AS Real de Bamako.
Mali's sports ministry is urging Fifa to act in order to avoid government interference.
Fifa rules outlaw state involvement with national football authorities and it has previously banned several African nations, including Mali and most recently Zimbabwe and Kenya, for doing so.
In 2018, a so-called normalisation committee was set up to conduct elections and manage the daily affairs of Femafoot as it was reintegrated into the Fifa fold.
This year's Femafoot elections are scheduled to take place on Tuesday 29 August.
Souce: BBC
