Yudhoyono said that Indonesian police arrested Egidio Lay Carvalho, Jose Gomes, and Ismail Moniz Soares.
The soldiers had reportedly entered Indonesia illegally.
Details of the arrest are unclear.
"They were arrested and detained based on arrest warrants issued by East Timor's government," Yudhoyono said.
"All ... three are East Timor's soldiers, not Indonesian nationals. For the time being, I cannot give more details. Indonesian police will give details after they completed the operation and investigation."
Return to Dili
The arrests came after statements made by Ramos-Horta soon after his return to Dili on Thursday, following his treatment at an Australian hospital.
He came close to dying after he was shot by masked fighters loyal to Alfredo Reinado, a rebel leader, in the pre-dawn attack of February 11.
Ramos-Horta claimed in a news conference on Thursday that "foreign elements" were involved.
He also said that an investigation into the attacks found that the fighters had contact with "elements" in Indonesia.
"The ongoing investigation shows a lot of contacts that Alfredo Reinado had with elements in Indonesia and I repeat - elements in Indonesia. In no way it implicates Indonesian government," he said.
Ramos-Horta also said that Yudhoyono had assured him that the Indonesian government would look into any evidence to see if individuals in the country had any part in aiding the rebels.
But on Saturday, Yudhoyono said Ramos-Horta should stop hinting that Indonesia was involved in the attacks as it could hurt relations between the two countries.
"I also [ask] the government of Timor-Leste [East Timor] to not issue statements which may seem like Indonesia is involved [in the attacks], because it can disrupt the good relationship," he said.
East Timor gained full independence from Indonesia in 2002.
The country has been unable to achieve stability since its hard-won independence from Indonesia, despite its oil and gas resources.