After spending last season on loan from Liverpool, the 24-year-old striker joined the Hammers permanently this summer in a deal worth £15.5million, plus a further £2million in add-ons.
Carroll penned a six-year deal, with an option for a further two, but has yet to turn out for Sam Allardyce's side due to injury complaints.
Much of last season's loan stay in east London was hampered by injuries and such problems continue to impact the England international.
"West Ham United can confirm Andy Carroll suffered an injury to his right foot during his return to full training today," said a statement on the club's official website, www.whufc.com.
"Although it is in the same part of his foot as his previous injury, it is a new injury and therefore there will be no prognosis until he has seen a specialist."
West Ham will give a further update on the club record signing when possible.