The Kenya midfielder was out of action for four months last season with a knee injury and has been told to rest amid fears it has flared up again.
Spurs officials say his absence from their 4-1 victory over Roma in San Diego was precautionary and staff were due to carry out checks on Thursday.
Wanyama suffered a knee injury on last summer's US tour and, after playing in their opening two games of the season, he was ruled out for four months – only returning in January.
According to the Daily Mail, the same knee flared up in training on Tuesday and he missed Spurs' 4-1 win over Roma in San Diego on Wednesday.
Whether he will make their next match, against Barcelona in Pasadena on Saturday, remains to be seen. Spurs must hope Wanyama, 27, won't be out of action for long. Eric Dier does not report back until August 4 along with fellow midfielder Mousa Dembele, who has been tipped for a move away.
Harry Winks has not travelled to the US as he recovers from an ankle operation.