"The match officials' report, which was handed over to the Zimbabwe team manager Mufaro Chiturumani after the Test concluded on Friday, cited concerns about the legality of the 30-year-old's bowling action," the ICC said in a statement.
Waller's bowling action will now be scrutinised further under the ICC process relating to suspected illegal bowling actions reported in Tests, ODIs and T20Is.
He is required to undergo testing within 21 days, and, during this period, Waller is permitted to continue bowling in international cricket until the results of the testing are known.