Currently, the recovery of materials from secondary sources is increasingly necessary because of the scarcity of materials. Significant amounts of rare earth elements (REE) are found in permanent neodymium-iron-boron (NdFeB) magnets, used in various electrical and electronic equipments, such as mobile phones. However, the estimated recycling rate for REEs is only 1%. Hydrometallurgical routes are the most commonly used for REE recovery from secondary sources. This route usually uses inorganic acids, which are expensive and toxic. Thus, in this work the leaching efficiency of organic acids (acetic and citric) in leaching the REE (neodymium and praseodymium) present in magnets of obsolete or defective mobile phones was evaluated. Different concentrations of acids, solid/liquid relations, times and leaching techniques (microwave, ultrasound and conventional) are also evaluated. The results indicate that acetic and citric acids have the potential to leach Nd and Pr. Microwave leaching was the most effective method, compared to ultrasound and conventional methods. In microwaves, citric acid at 0.5 M (ratio s/l 1/100) leached 57% of Nd and 58% of Pr. Acetic acid at 0.5 M (s/l ratio—1/100) leached 48% of Nd and 65% of Pr, in 15 min. Furthermore, both citric acid and acetic acid also leached high percentages of iron (51% and 72%, respectively).