Britain, France, the United States and Australia all urged their nationals to be vigilant, although they stopped short of advising against travel to the former junta-ruled country.
"There is a high threat from terrorism," the British foreign office said in updated advice following a blast at the Traders Hotel in the city late Monday.
"Attacks could be indiscriminate, including in places frequented by foreigners... The motivation for the attacks is at present unclear," it added.
Observers said the small explosions were likely aimed at stoking panic and harming reform efforts by the new quasi-civilian government, rather than causing mass casualties.
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No group has claimed responsibility for the blasts, which bore some similarity to explosions seen under the former junta, which usually blamed armed exile groups or ethnic rebels.
The injured American was taken to hospital with wounds to her thigh and her hand after a blast tore through her room at Traders, part of the Shangri-La group, which is popular with foreign tourists and business people.
An unnamed source from the Karen National Union (KNU) rebel group told AFP that the man was one of its members, adding that he could have been trying to show "dissatisfaction" with a tentative ceasefire deal between the rebels and the reformist government.
But KNU vice president Naw Zipporah Sein denied the group was involved.
The US embassy in Yangon urged caution, but said there was currently "no indication" that Americans were specifically targeted.
Police said several other people have been questioned in connection with the series of blasts in Yangon and other cities that have killed two people and injured at least four since Friday.
State media reported that a further suspect was being sought by authorities.