Michael Young delivered his letter to Ms Sturgeon in person at Holyrood.
His family is campaigning for the NHS to support the use of Translarna, a new drug available in other EU countries.
The drug is currently being assessed by the Scottish Medicines Consortium (SMC), a process Ms Sturgeon said she could not interfere with.
Michael, from Larbert in Stirlingshire, has Duchenne muscular dystrophy - a severe condition causing irreversible muscle damage. Few born with it survive to their 30th birthday.
He took part in a clinical trial during the development of Translarna, a drug tackling the underlying causes of the disease which has been approved by the EU.
Michael wrote to Ms Sturgeon explaining about his condition and asking for her to "help boys to keep walking".
The first minister said she was able to explain to Michael that the assessment procedure had to be "entirely independent of government".
She also criticised the pharmaceutical firm which developed the drug, PTC Therapeutics, for taking time to submit its proposal to the SMC.
Ms Sturgeon said: "It was an absolute delight to meet Michael today, he's a really impressive and brave young man campaigning not just for himself but for other young boys with Duchenne.
"We were disappointed that the pharmaceutical company took so long to put forward a submission on this drug to the Scottish Medicines Consortium and we have previously urged them to put forward a good quality submission with a fair offering of price.
"This government has taken a number of significant steps to improve access to new treatments for patients with rare conditions."
Robert Meadowcroft, chief executive of Muscular Dystrophy UK, said: "We are delighted that Michael was able to deliver his amazing, heartfelt letter to Nicola Sturgeon in person, an opportunity that doesn't come every day.
"The meeting means a great deal to the Youngs, and other families who live with Duchenne muscular dystrophy across Scotland.
"It is wonderful that the first minister gave up her time in support of Michael, and we hope their meeting will lead to positive discussions with the Scottish Medicines Consortium about Translarna."
The Scottish Medicines Consortium is expected to come to a decision on the use of the drug in March.
A nine-year-old boy with muscular dystrophy has met with First Minister Nicola Sturgeon after he wrote to her campaigning for a new treatment.