Short answer: usually yes. If a retail shop publicly plays copyrighted music (even quietly as “background”), you generally must have a public‑performance license unless a narrow statutory exemption applies. (copyright.gov)

Key points and what to do

• Who enforces it: copyright owners license public performances through performing‑rights organizations (PROs) such as ASCAP, BMI and SESAC. Most businesses use blanket licenses from those PROs (many businesses carry more than one because each PRO covers different songs). (bmi.com)
• Consumer streaming apps: consumer subscriptions (Spotify, Apple Music, YouTube, etc.) are licensed only for personal use and do not cover playing music in a commercial setting. Using them in a store can cause liability. (bmi.com)
• Common alternatives: (a) buy blanket licenses from the PROs that represent the music you’ll play; (b) subscribe to a commercial/background‑music service that holds the PRO licenses for business use (many such services advertise that they handle licensing); or (c) play only public‑domain music or music you have a direct license to use. (bmi.com)
• Narrow exemption (Fairness in Music Licensing Act): retail stores that only receive radio or TV transmissions may be exempt if they meet strict size/equipment rules (for most non‑food retail: under 2,000 gross sq. ft. (excl. parking) OR, if ≥2,000 sq. ft., stay within loudspeaker/TV limits). Restaurants/bars have different thresholds (3,750 sq. ft.). The exemption applies to receiving broadcast radio/TV only — it does not cover playing CDs, playlists or digital files you control. Check the statute for exact limits. (law.cornell.edu)
• Consequences of not licensing: copyright owners/PROs can seek damages and injunctions. Statutory damages in U.S. civil cases run (generally) from about $750 to $30,000 per work — and can go up to $150,000 per work for willful infringement. (copyright.gov)

Practical next steps

1. Decide how you’ll play music (radio/TV only vs. recorded playlists vs. live music/DJs).
2. If you’re likely outside the FMLA exemption, contact ASCAP/BMI/SESAC (or use a commercial background‑music provider) to get the correct business license(s). (bmi.com)
3. Keep proof of any licenses/subscriptions on file and make sure any music service you use explicitly says it covers business/public‑performance rights.

If you want, I can: (a) look up contact/license pages for ASCAP/BMI/SESAC, or (b) check whether a specific business music service explicitly covers PRO/public‑performance licensing. Which would you prefer?