Pell is the highest-ranking Catholic cleric to be found guilty of child sex abuse.
The 78-year-old, who was Pope Francis's finance chief and one of his closest advisers, was convicted last December on one charge of sexual penetration of a child and four charges of committing an indecent act with or in the presence of a child.
Authorities are investigating whether the letter, dated August 1 and posted on Twitter, breaches rules forbidding prisoners from posting on social media or using the internet, or asking others to post on their behalf.
The letter was posted on Friday night on a Twitter account called Cardinal George Pell Supporters.
A spokeswoman from the Department of Justice of Victoria state, where Pell is in prison, said the letter was being investigated.
"(The department) will thoroughly investigate this social media activity," the spokeswoman said. "Any prisoner found to be contravening prison regulations faces disciplinary action."
The spokeswoman did not confirm whether the letter was written by Pell.
He was found to have raped a 13-year-old choirboy and sexually molested his friend in the sacristy of St Patrick's Cathedral in Melbourne in 1996 when he was newly installed as the city's archbishop. He abused the first boy again about a month later.
In March, he was sentenced to serve at least three years and eight months in jail.
Pell has appealed against the conviction and is awaiting a ruling from the Court of Appeal following a two-day hearing in June.
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