The BBC reported that Ighalo was dropped because of fears the coronavirus outbreak could lead to his being refused entry back into the UK.
Nigerian born Ighalo, 30, flew to Manchester from China last weekend after signing on loan from Shanghai Shenhua.
The coronavirus has claimed 722 lives and restrictions could be placed on travelers who have been in mainland China within the past fortnight.
“Odion will stay in Manchester, because he arrived from China in the last 14 days,“ manager Ole Gunnar Solskjaer told MUTV.
“Because of the situation in China, we’re not sure if he’d be allowed back into England if he leaves the country again.
“He’s staying here working with a personal coach, individual programme and his family then can settle in England as well. That’s a plus.
“Of course he might have liked to have come with the players and get to know them, but with the risk [of potential border restrictions tightening], we don’t want to take that.”
United, who will stay in Marbella when they head on their warm-weather training camp this weekend, described the decision as a “precautionary measure”.