The ban was ordered by the adjudicatory chamber of the Fifa ethics committee, which is currently studying a report into bin Hammam's possible role in influencing the award of the 2022 World Cup to Qatar, a Fifa statement said.
In a statement, Fifa said the Mongolian would be barred from "any kind of football-related activity at national and international level" during his five years' of punishment.
Buyannemekh "solicited and accepted payments" from disgraced former Asian Football Confederation chief and Fifa executive member bin Hammam, the statement said.
Fifa said the offences occurred during the 2009 elections for its executive at the Asian Football Confederation (AFC) congress, as well as during the Fifa presidential election in 2011.
Buyannemekh is currently a member of the AFC executive committee as well as other key committees in the regional group.
He is the second top Asian football official to be banned over alleged payments from bin Hammam.
One year ago, Sri Lanka's then football chief, Manilal Fernando was banned for life over bribery and corruption charges.
Fernando was a close ally of bin Hammam who resigned from FIFA's executive and as AFC president in December 2012, days after the governing body launched a new corruption inquiry against him.
He had earlier successfully appealed against a life ban over other corruption allegations.
British media reports have said bin Hammam also spent millions of dollars to seek support from Asian and African officials for his homeland Qatar, which won a controversial 2010 vote to secure the 2022 World Cup.
Qatar has strongly denied any wrongdoing or any link to bin Hammam's actions.