News of the arrests came a day after the authorities detained a senior official from international aid agency Medecins Sans Frontieres (MSF) in Sudan on Monday, whose remote region of Darfur has been plagued by more than two years of bloodshed.
The aid worker held on Tuesday was also from MSF Holland, which published a report in March detailing about 500 cases of rape over a period of four and a half months in Darfur, where a rebellion has raged since early 2003.
Sudan's top UN envoy in Sudan, Jan Pronk, "deplored" the arrests of the two MSF officials and said he would raise the issue with Sudanese President Omar Hassan al-Bashir.
The country director of MSF Holland, Paul Foreman, was detained on Monday and released on bail after a day of questioning. He said he had been charged with spying, publishing false reports and undermining Sudanese society.
"I have now been formally charged," Foreman said, adding his colleague Vince Hoedt was still being questioned.
Hoedt, Darfur coordinator for MSF Holland, was arrested in the western region on Tuesday. He was flown back to Khartoum and immediately taken away by security forces. Journalists were prevented from filming his arrival.
A UN investigation has found
evidence of mass rape in Darfur
"I have been officially arrested but there are no official charges as yet," he earlier told Reuters from Darfur.
It was not immediately clear whether the arrests of the two MSF officials were in any way linked to the translator case.
Pronk said the authorities had arrested a translator who went with Annan to listen to rape victims in Darfur's largest camp on Saturday, despite government promises no one would be harassed.
Human Rights Watch has said in a statement the authorities should be arresting war criminals in Darfur, not aid workers. It said at least 20 aid workers have been arbitrarily arrested in Darfur over the past six months.
"This is a perfect illustration of how far the Sudanese government is prepared to go to silence criticism and deny its own responsibility for massive atrocities in Darfur," Peter Takirambudde, Africa director for the rights group, said.
A UN-appointed commission of inquiry earlier this year found evidence of mass rape during the rebellion in Darfur.
Annan talked to both refugees
and aid workers in Darfur
During his visit on Saturday, Annan heard aid workers complain of problems with the authorities.
He also listened to refugees who complained of harassment and said they wanted guarantees from Annan that they would not be arrested for speaking with him.
The state minister of humanitarian affairs, Mohamed Yousif Abdalla, publicly assured them of their safety.
Against that promise a Sudanese translator has been arrested," Pronk said.
Annan had entered a reed hut to talk with rape victims, one of whom was pre-pubescent, aid workers said. The translator accompanied him and was later arrested.