(1) Background: Burden scales are useful in estimating the impact of interventions from patients’ perspectives. This is overlooked in sodium diet/heart failure (HF). The aim of this study is to develop and validate a specific tool to assess the burden associated with low-sodium diets in HF: the Burden scale In Restricted Diets (BIRD). (2) Methods: Based on the literature and reports from patients, 14 candidate items were identified for the following dietary-related domains: organization, pleasure, leisure, social life, vitality, and self-rated health. The validation study was conducted prospectively. The questionnaire was refined via item reduction according to inter-item correlations and exploratory factor analysis. Internal consistency was determined using Cronbach’s alpha (Cα) and convergent validity by assessing correlations between BIRD and the health-related quality of life (HRQoL) Minnesota Living with HF questionnaire (MLHF). (3) Results: Of the 152 invited patients, 96 (63%) returned the questionnaire. The median score was 6.5 (IQR 2.0–14.0). The results showed good acceptability (non-response rates/item from 2.0% to 12.1%), an excellent internal consistency (Cα = 0.903) and a good convergent validity (rhos = 0.37 (physical), 0.4 (mental), and 0.45 (global); all p < 0.05). (4) Conclusions: BIRD demonstrates good psychometric properties and is useful to quantify the burden associated with sodium restriction. It may help optimize dietary interventions and improve the overall management of patients with HF.