Western and Afghan troops are among "a significant number of casualties", a Nato spokesman said.
Gen Daud was former military commander of the Northern Alliance, the Afghan forces who fought the Taliban.
Afghanistan has seen a series of attacks in recent months by militants on police and military targets.
High-level meeting
The latest attack will be seen as significant because it has struck an area of the country's north which has been seen as relatively secure.
The BBC's Paul Wood in Kabul says the attack is a propaganda victory for the Taliban and a blow to wider, counter-insurgency efforts.
Gen Daud was in charge of all interior ministry forces in northern Afghanistan and is the most senior figure to be killed so far in a Taliban "spring offensive".
He was highly thought of by Nato because he got the job done, our correspondent adds.
Gen Daud was a former deputy interior minister for narcotics.He also served as the bodyguard to Ahmad Shah Massoud, who commanded the Northern Alliance.
The attack occurred at the compound of Takhar provincial governor Abdul Jabar Taqwa, in Taloqan, where officials were having a meeting.
The bomber, wearing a police uniform, was waiting in the corridor when the officials came out, our correspondent says.
Seven people were killed in the explosion, including Gen Daud and the provincial police chief Shah Jahan Nuri, a spokesman for the governor's office said.
At least 10 Afghans were injured, including the provincial governor, he added.
The Taliban has claimed it carried out the attack.
The governor's spokesman said three German troops were killed in the bombing, but this has not been confirmed by Nato.
A spokesman for the Nato-led International Security Assistance Force (Isaf) said there were reports of "a number of casualties" but did not give details.
Among those who survived the blast was General Markus Kneip, the top commander of foreign troops in north Afghanistan.
An Isaf spokesman confirmed that Gen Kneip was in the compound at the time but "was not killed".
German media reported that the general was wounded, along with three of his soldiers, while two German troops were killed.
German troops are based in neighbouring Kunduz province, and have oversight of Takhar.
The province was until recently a relatively quiet area of Afghanistan, but tensions rose in May after a Nato-led night raid in Taloqan which killed four people.
A crowd of 2,000 people took to the streets to protest against the attack, claiming the victims were civilians.Nato said the group were insurgents.
Police opened fire on the demonstrators, killing 12 people and wounding 80.
A smaller protest the following day saw the provincial police chief's compound attacked.