The group has recently targeted the website and Twitter account of watchdog organization Human Rights Watch and the Twitter account of French news service France 24.
The BBC Weather Twitter feed began posting unusual messages in the early afternoon, ranging from offensive to humorous and often making reference to Syria and Middle Eastern politics.
One tweet declared: "Long Live #Syria Al-Assad #SEA."
Soon after the Syrian Electronic Army said it had hacked the account along with several others.
"@BBCarabicOnline & @BBCWeather & @Bbcradioulster was hacked by Syrian Electronic Army #SEA #Syria," the group said in a tweet.
The hackers' tweets have since been removed from the BBC Weather account and replaced by a tweet apologizing to followers.
The account of BBC's Radio Ulster service, which covers parts of Northern Ireland, also posted a tweet apologizing for abnormal service.
"We are aware that in the past few hours several BBC Twitter accounts have been hacked. We are actively working on this and expect it to be resolved shortly," a BBC statement said.