The bombs were planted at the Institutional Revolutionary Party's (PRI) headquarters, the federal electoral tribunal and a Scotia Bank Inverlat building, said the city's public security secretary, Joel Ortega.
The bombs exploded nearly simultaneously, Ortega said. No note claiming responsibility for the blasts was found, he added.
A fourth bomb targeting a branch of Scotia Bank Inverlat did not explode, but was easily identified, with a label painted on its side: "Bomb Danger".
"The five-kilogram (11-pound) bombs had small alarm clocks and a detonator ... (and were) made with a certain kind of fertiliser, which, mixed with diesel fuel, can be a powerful explosive, as we saw last night," Ortega said.
Ammonium nitrate fertiliser is commonly used in mining and industry, as well as bombers.
The Mexican government condemned the attacks.
"We categorically reject these criminal acts aimed at scaring the population and we will work tirelessly to guarantee permanently the population's security," President Vicente Fox said.
The facade of a PRI auditorium was destroyed as well as a bust of party founder and former president Plutarco Elias Calles.
The exterior of the building housing the electoral tribunal's press relations office suffered serious damaged.
The third bomb damaged the bank building and television images showed that windows of a nearby residential building were shattered.
Telephone calls prior to the explosions alerted the police to the bombs' locations, officials said.

Copyright AFP (Agence France-Presse), 2006