A local official, who spoke on condition of anonymity, said at least eight people were left dead in the attack in Mehtarlam, in the eastern Laghman province.
Laghman governor spokesman Sarhadi Zwak placed the death toll at 16, with another 39 wounded.
No one has claimed responsibility for the attack but suicide bombings are a hallmark of the Taliban's war against foreign and Afghan security forces, now in its fourteenth year.
The insurgents are able to mount regular attacks across swathes of the country, particularly southern and eastern provinces.
Thursday's funeral was being held for a police commander and three other people who were killed in a roadside bomb blast, according to Zwak.
Afghanistan saw a surge in violence last year as international forces wound down their combat mission, which began in 2001. It has now been downgraded to support and training duties to help the Afghan army and police.
About 17,000 foreign soldiers, most of them from the US, will remain in Afghanistan as part of the new mission.
But US troop numbers are set to halve within 12 months and fall to almost nothing in two years.
Civilian casualties rose 19 percent from the previous year to a record high in 2014, with nearly 3,200 civilians killed and over 6,400 injured, according to a UN report released in December.
Casualties among children had jumped a third and among women by 12 percent by the end of November, in the deadliest year for non-combatants, said the report.