United have been accused of offering very large sums to the parents of the teenager, who has captained the national team at under-16 level, to induce him to end a contract he has until the end of this season.
In an angry statement Le Havre said: "This act is even more unacceptable as it comes from a club with such stature."
But a United spokesman told BBC Sport: "It is complete nonsense. Everything has been done within UEFA guidelines."
Le Havre, who were relegated to the French second division last season, claim an agreement between the club, Pogba and his parents was in place for the player to stay until the end of the 2009/2010 season.
A statement - under the heading 'Manchester United steal Paul Pogba from HAC (Le Havre)' - on the club's website said: "Le Havre wishes to express its indignation regarding the dealings of Manchester United's directors in relation to the young Paul Pogba.
"The player and his parents refused to keep the arrangement because Manchester United offered very high sums of money to the parents of the (player) with the aim of obtaining the transfer of their son.
"At a time when numerous parties - including at European Union level, governmental (level), or within FIFA or UEFA - are speaking out against the 'trading of minors,' Manchester United does not hesitate to uproot a 16-year-old kid."
Players from European Union countries are able to move to Britain on academy or scholarship contracts at 16, and to sign full professional contracts at 17.
By signing a player under the age of 18, the buying club minimises the level of compensation the selling club will get.