Brazil takes on Peru on Thursday hoping to make it two wins in two games, before Argentina faces Uruguay on Friday.
"Nike was deeply disturbed by sexual assault allegations made by one of our own employees against Neymar Jr.," a Nike spokesperson said on Thursday.
Brazilian has made clear he wants to leave Paris-Saint Germain and return to Barcelona, the team he left two years ago.
The 46th edition of the tournament gets underway on Friday and promises to be one of the most even in years.
Brazil hosts the Copa America this year but has not won the tournament in 12 years and will be without Neymar.
Neymar could leave Paris Saint-Germain, while Real Madrid want Eden Hazard.
The Brazil star has been widely criticized for going to ground far too easily.
The five-time Ballon d'Or winner will reportedly earn $35 million every year in Italy.
The 411 on this summer's biggest sporting event.
The campaign will see 10,000 school meals donated each time Neymar or Messi score at this World Cup.
Paris Saint-Germain is enjoying an 11-point cushion at the top of the French table.
The Brazilian only just left the club, joining Paris Saint Germain for £199 million in the summer.
The Portuguese coach's agent has reportedly been speaking to another club.
Real Madrid host Tottenham Hotspur in the Champions League group stage on Tuesday night.
The world transfer record was broken this summer, when PSG paid £199 million for Neymar.
United completed its deals early in the transfer window.
Any of these signings would have been massive.
The club is on the lookout for a replacement for the 25-year-old after Barcelona reportedly offered $156m.
The Spanish giant is reportedly willing to pay £120 million for Coutinho, to replace Neymar at the Camp Nou.