Police Scotland said two men - one from Aberdeen and one from Paisley - had been arrested and charged with sexual offences against children.
The referrals came via the charity NSPCC, the SFA and directly to police.
Officers said it was the most complex investigation since the Police Scotland child abuse unit was set up in 2015.
The unit, along with other experienced detectives, are in the midst of a major inquiry into allegations that children were abused in the sport following reports from several high profile players.
Det Ch Insp Sarah Taylor, who is heading the investigation, told BBC Scotland she expected the scale of the investigation to grow.
"Up until today, we've had 130 separate reports with information about child sexual abuse within football and that is since the end of November.
"So, in such a short space of time, we've received a number of reports. That indicates to me that this is a large-scale complex investigation that we're undertaking."
Ms Taylor said she was encouraged by the number of reports as it showed people had the confidence to come forward to the authorities.
She also said that unlike Operation Hydrant south of the border, which is also looking into allegations of abuse in other sports, the Scottish investigation was focussing on football.
She added: "However, I wouldn't discourage people from contacting the police if they have suffered abuse - sexual or physical - in any other environment.
"This is a major investigation and we've reacted to it by deploying a number of officers to be dedicated solely to this investigation.
"It's complex because we're dealing with a number of perpetrators and a number of people who've reported abuse, so for me it's about trying to piece that jigsaw together."
A police investigation into allegations of child abuse within football has received 130 referrals since it got under way in November.