Atiku Abubakar, from the Peoples Democratic Party (PDP), claimed Buhari's ruling All Progressives Congress (APC) had offered cash inducements to voters.
"This is what the APC is doing. They are buying PVCs (permanent voter cards). They will come to you and give you 10 naira, 20 naira, 50 naira to buy your PVC," he told supporters.
"They are buying your future," he was quoted as saying in local media after a campaign rally in the central city of Ilorin on Wednesday.
There was no immediate response from the APC but civil society groups, local and foreign observers have previously voiced concerns about leading parties offering cash for votes.
The practice of using PVCs bought from voters to rig elections was said to have been widespread during recent governorship polls in the southwestern states of Ekiti and Osun, both won by the APC.
In Ekiti, both the APC and the PDP were accused of offering voters 3,000 to 5,000 naira ($8-13, 7-12 euros).
During the PDP presidential primaries in October, some candidates, including Abubakar, were accused of offering financial inducements to delegates.
Abubakar, a former vice president to Olusegun Obasanjo between 1999 and 2007 who used to run the country's customs service, has also been accused of widespread corruption.
He denies the allegations and has challenged his detractors to produce concrete proof.
Buhari, 75, was elected in 2015 on promises to tackle endemic corruption, end Boko Haram's deadly Islamist insurgency and boost the economy.
He is hoping for a second term of office but Abubakar, 72, said: "In terms of corruption, Nigeria is worse off today than we were in 2014.
"In terms of economy, we are the poorest country in the world today. In terms of insecurity, we are the most insecure than at any other time in history."