The 33-year-old, who was a standout in Australia's recent one-day series against Bangladesh, apologised for "failing to meet the standards" expected of her.
Cricket Australia said in a statement she breached "requirements under the Sports Science and Sports Medicine guidelines with regard to prescription medication".
"This relates to a single incidence which occurred while out of competition and was not for performance enhancing purposes," it added.
"We will continue to provide appropriate support to Megan and reinforce the standards and responsibilities expected of everyone representing our game."
Her two-match ban will see Schutt miss Thursday's third and final T20 against New Zealand and the Adelaide Strikers' opening game of the Women's Big Bash League later this month.
"I fully accept the penalty handed down and apologise for failing to meet the standards expected of me," said Schutt, who has played 114 ODIs and 126 T20s for Australia.
"I'm sorry for the attention this has caused and appreciate the support I've received."