The Dutchman collided with Inter's Lucio and briefly lost consciousness before being taken to hospital.
However, a scan gave Stekelenburg the all-clear, and he had two stitches in a head wound.
His agent Robert Jansen said he is due to be released later on Sunday, and he and Roma will then look at the incident to decide whether they want to see Lucio punished.
"I spoke to Maarten. He is well. He had a good night and tonight he will leave hospital," Jansen said on www.vocegiallorossa.it.
"We are not thinking of Lucio's gesture or whether it was intentionally or unintentionally or he could have prevented it. The only important thing is Maarten's condition.
"Once he recovers, we will consider with Roma the case and the eventual responsibility of defender Lucio. We are only focused on Maarten's health."