Officials learned of the alleged encounters while investigating a tabloid newspaper report that she had been beaten.
The guard, 50, was suspended and could be fired, a prison spokesman said.
Smith allegedly had sex with the guard at the Women's Correctional Institution in May and June. There was no evidence she was beaten and no indication that the guard forced her to have sex, officials said.
Calls to attorneys for Smith and the guard were not immediately returned Wednesday.
Smith's 3-year-old and 14-month-old sons drowned in 1994 after she let her car roll into a lake.
She claimed at first that the boys had been taken in a carjacking and pleaded on national television for their return. Nine days later, when no sign of the boys turned up, she confessed, and the bodies were found.
She was convicted of murder in 1995. A jury spared her the death penalty.
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