The seven-year-old carrying a knife was caught by officers earlier this year while a pair of nine-year-olds were found in possession of blades during 2010 in the Lothians.
Police figures also show a pair of nine-year-olds were charged with possession of offensive weapons after being found wielding a snooker cue and a wooden coat stand.
The age of criminal responsibility in Scotland is eight, and youngsters aged below that are not charged with crimes.
Meanwhile, the number of under 18s caught with knives rose between 2009 and last year, increasing from 55 to 69.
Between January and the start of July, another 45 charges were brought against juveniles.
Cases of possessing an offensive weapon amongst under 18s dropped during the same period, from 164 to 141. The figure was 61 cases for the first six months of this year.
Edinburgh Central MSP Marco Biagi described the cases as “shocking”.
He said: “There is no denying that these are shocking examples. Any case of a seven-year-old carrying an offensive weapon is a tragedy itself.
“I can only guess at the extent of the failings in home life and parenting that could have led to that situation.
“I hope that in every one of these cases police, social work and the education system took immediate and firm action.
“We should also all take a moment to pause and remember that these cases do not represent young people as a whole.
“It would be unfair to judge an entire generation on the failings of the worst individuals.
“Knife crime is a horrific experience for those who become victims regardless of the age of the perpetrator.”
Research from the Edinburgh Study of Youth Transition and Crime released earlier this year showed almost a third of teenagers in Edinburgh admitted to walking the city’s streets carrying a knife.
The academic study, which gathered information from 4000 youngsters, revealed that 14-year-olds were the biggest problem group, with a quarter in the Capital admitting they had carried a knife.