Apricot breeding programs could be strongly improved by the availability of molecular markers linked to the main fruit quality traits. Fruit acidity is one of the key factors in consumer acceptance, but despite its importance, the molecular bases of this trait are still poorly understood. In order to increase the genetic knowledge on the fruit acidity, an F1 apricot population (‘Lito’ × ‘BO81604311’) has been phenotyped for titratable acidity and juice pH for the three following years. In addition, the contents of the main organic acids of the juice (malate, citrate, and quinate) were also evaluated. A Gaussian distribution was observed for most of the traits in this progeny, confirming their quantitative inheritance. An available simple sequence repeat (SSR)-based molecular map, implemented with new markers in specific genomic regions, was used to perform a quantitative trait loci (QTL) analysis. The molecular map was also anchored to the recently published apricot genome sequence of ‘Stella.’ Several major QTLs linked to fruit acidity-related traits have been identified both in the ‘Lito’ (no. 21) and ‘BO81604311’ (no. 13), distributed in five linkage groups (LG 4, 5, 6, 7, and 8). Some of these QTLs show good stability between years and their linked markers were used to identify candidate genes in specific QTLs genomic regions.