Only two days after joining the Ligue 1 club from AC Milan, Menez lost part of his right ear during a tangle with Lorient's Didier Ndong.
The incident occured as the Lorient midfielder stood on the 29-year-old's head, accidentally taking out a chunk of his ear in the process.
In an official club statement, Lorient confirmed that the former Paris Saint-Germain forward would require surgery on the injury.
Ndong also offered his apologies to the former French international following his part in the incident.
'I offer my apologies to Jeremy Menez and Bordeaux.
'I give him my full support for the coming days and hope to see him very quickly on the lawns of Ligue 1 .'
Menez signed a three-year contract with the French club on Monday after two seasons in Serie A.
He lasted only 15 minutes of the friendly, in which Bordeaux ran out 3-1 winners.
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