"The bomber followed crowds of the wounded into the hospital and detonated himself in an effort to get the police chief as well," our correspondent said.
Major-General Abdul Hussein al-Shimmari, the police chief, escaped unharmed but a number of his personal security team were wounded.
The attacks, coming despite heightened security across the country ahead of Sunday's vote, were the deadliest to hit Iraq in nearly a month.
"Diyala [Baquba is the capital of the Diyala province] has been quiet in the lead up to the election. It was, of course, one of the most violence-stricken provinces back in 2007, but this is a dramatic escalation of violence there," McNaught added.
The bombings follow a threat by Abu Omar al-Baghdadi, al-Qaeda's leader in Iraq, that he would disrupt elections by "military means".
Before hitting Baquba's main hospital, bombers in explosives-laden vehicles targeted the city's provincial housing department's offices and a nearby intersection at around 9:30am (06:30 GMT).
The first vehicle crashed through the entrance to the provincial housing department's compound, which sits next to a police station, before exploding.
Moments later, at a nearby traffic intersection, a suicide bomber detonated explosives packed into his vehicle, triggering a powerful blast.
The hospital bombing occurred a short time later.
Iraqis go to the polls on March 7, the second such vote since Saddam Hussein, the former president, was ousted in 2003.
|The three co-ordinated attacks damaged several buildings including a hospital [AFP]
Al Jazeera's Mike Hanna, reporting from Baghdad, said there had been a spike in violence across the country in the lead-up to the election.
He said a number of measures have been taken to ensure security.
"There will be 48-hour period of calm before the voting takes place during which no campaigning can happen. There are also indications that there will be a curfew in major areas throughout the country.
"The safeguards are in place but there have been security safeguards in place for a period of time ... Bombings such as [in Baquba] today and bombings in Baghdad in recent weeks indicate that no matter how tight the security, bombers seeking to disrupt the election process could find a way."
Last Sunday, Iraq's national security adviser told the AFP news agency that security forces had found and prevented at least 10 vehicle bombs in the past month as al-Qaeda and other rebel groups sought to target the election.
Safa Hussein said most of those bombs, which would have caused "very major damage", would have targeted Baghdad.
The parliamentary elections are seen by Washington as a crucial precursor to a complete US military withdrawal from Iraq by the end of 2011.
The UN envoy to Iraq has said that while he was concerned by the level of violence, it had not affected preparations for the elections.