Ukraine has not commented on the bombing.
The FSB said the suspect had been recruited by Ukraine in 2023, and had driven to Moscow in September that year.
Russian media also reported that the FSB had released a video showing the detained man giving an apparent confession, as well as footage of his arrest and of the bomb’s components.
The Kremlin had on Friday blamed Ukraine for the attack, saying Kyiv “continues its involvement in terrorist activities inside our country”.
Gen Moskalik had represented Russia in talks with Ukraine in Paris in 2015, which resulted in the failed Minsk agreements which aimed to end the fighting in the Donbas region between Ukraine and Russian-backed separatist forces that started in 2014.
Russia launched a full-scale invasion of Ukraine in February 2022.