MBC television reported that Roh said in the note that things have been "difficult" and he felt he had made "too many people suffer".
The note also said Roh wanted his body cremated, according to the report.
MBC did not say how it obtained the note.
A spokesman for the national police agency said: "Ex-president Roh fell down a mountain.
"He was transported to a hospital where doctors said he was dead on arrival. We're investigating whether he fell by accident or committed suicide."
The tragedy occurred after Roh, 62, went hiking with an aide near his retirement home at Bongha in Gimhae district near the southeast coast.
Moon Jae-In, a former chief presidential secretary, told journalists: "President Roh jumped off a rock in the mountain behind Bongha village."Head injuries
Roh left a brief suicide note for his family, Moon said.
Yonhap news agency said Roh suffered severe head injuries and died after being moved from a smaller hospital to a larger one in the city of Busan.
Busan National University Hospital said in a statement that Roh was pronounced dead at 9:30am (00:30GMT) from head injuries.
TV footage showed the rocky cliff from which Roh fell, and forensic experts were searching the pine-clad terrain where the incident occurred.
Roh, who had been questioned by prosecutors in the graft case, publicly apologised for his family's involvement but had not admitted personal wrongdoing.
In an unrelated graft case, Roh's elder brother was last week jailed for four years for taking more than $2m in bribes during his sibling's term in office.
Roh Gun-Pyeong was sentenced for accepting about $2.36m to arrange the acquisition of brokerage Sejong Securities by the state-run national agricultural co-operative federation.
Donald Kirk of the Christian Science Monitor told Al Jazeera that Roh had left a mixed legacy.
"He did have the reputation of a Mr Clean. In his younger days he was a labour lawyer, battling for workers."
"He had a big reputation as a liberal and as incorruptible," Kirk said.
"He did fight for reconciliations with North Korea, he did meet North Korea's leader at a summit in October 2007 several months before stepping down.
"He was terribly unpopular while being the president because of economic issues, but I don't think he can be regarded as a failure and I actually think there is tremendous grief because of his passing."
Lee Myung-bak, South Korea's president, said on Saturday that the news was "truly hard to believe" and called Roh's death "sad and tragic", Lee Dong-kwan, a presidential spokesman, said.