Michael Adebowale, 22, was formally taken into police custody as the family of his co-accused, Michael Adebolajo, issued a statement expressing their "profound shame and distress" over the murder.
Soldier Lee Rigby was hacked to death in broad daylight last Wednesday near a barracks in Woolwich by two men who later spouted Islamic extremist rhetoric at passers-by.
Both Adebowale and Adebolajo, 28, were injured in police fire at the scene and were held at separate London hospitals under armed guard until they were well enough to be questioned.
Detectives have 24 hours to question him before they have to apply for an extension. After a total of 96 hours, they must decide whether to charge him or release him.
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Adebolajo, who was captured in amateur footage after the attack claiming he murdered the soldier because British troops were killing Muslims, remains in stable condition in hospital.
In a statement, his relatives sent their "heartfelt condolence" to the family of the murdered 25-year-old, which includes his two-year-old son Jake.
They said there was "no place for violence in the name of religion or politics".
"However, as a family, we wish to share with others our horror at the senseless killing of Lee Rigby, and express our profound shame and distress that this has brought to our family."
They said they "wholeheartedly condemn" terrorism, and "fully expect" that the soldier's killers will be brought to justice.
Both Adebolajo and Adebowale, Muslim converts from Nigerian Christian families, are believed to have been known previously to the British intelligence services.
Adebolajo was arrested in Kenya in 2010 and questioned over alleged links to neighbouring Somalia's Al-Qaeda-linked Shebab militant group, Kenyan authorities have confirmed.