Wheezing and cough are common case scenarios that pediatricians encountered in their office practices. Although a bronchogenic cyst is an uncommon condition, it is essential to be considered in the differential diagnosis of a chronic cough and wheezing among young children who fail to respond to appropriate medical treatment. A 28-month-old girl was referred to our pediatric pulmonology clinic with persistent symptoms of a cough and wheeze unresponsive to standard asthma therapy. This presentation prompted us to undertake a detailed diagnostic evaluation. The evaluation exposed a cystic mass in the middle mediastinum compressing the trachea and left main bronchus. The cyst was excised and confirmed pathologically to be a benign bronchogenic cyst. Subsequently, the patient recovered well and had been free of respiratory symptoms during follow-up visits. This report highlights one of the rare causes of wheezing and cough in young children and emphasizes the importance of considering it in the differential diagnosis of a child presenting with refractory asthma-like symptoms. This is important for early diagnosis and management and to avoid unpredictable complications of this treatable condition.