Several factory workers were injured by police when 4,000 workers clashed with police outside the plant’s premises in Kampong Speu province, Nike said.
Following the violence, eight workers and trade union members were detained and hundreds of employees were dismissed.
The Cambodian government should "open an inquiry using credible, independent third parties to determine the cause of the incident," the company’s vice president Hannah Jones said in the letter dated May 30.
“In addition, we urge the Cambodian government to consider the appropriate support for the injured workers,” it said.
The commerce and labour ministers did not respond to requests for comment. Free Trade Union leader Chea Mony said authorities had done nothing, so far, to end the labour conflict.
Rights groups said Nike's request was only a response to pressure.
"The Free Trade Union sent an open letter to Nike and the US Embassy last week," Solidarity Center Cambodia director David Welsh told dpa.
"Violence by security forces is an important issue. The right to strike is part of the Cambodian constitution. As Election Day approaches, the government has to take the request seriously, even if it will not undertake legal operations," he added.
The Free Trade Union is viewed as siding with the political opposition.
The workers were striking to demand a 14-dollar increase to their 74 dollars a month.