The Delaware Division of Public Health says the 55-year-old man came into contact with all of those people in shelters.
The investigation will begin on Monday, but authorities have not said exactly where they will begin.
The Centers for Disease Control will assist the DPH.
Tuberculosis is a bacterium that is inhaled into the lungs. The bacteria are released into the air when a person infected with TB coughs. People with TB disease are most likely to spread it to people they spend time with every day, such as family members, friends and coworkers.
Signs and symptoms of TB include a strong cough that lasts more than two weeks, coughing up blood or sputum, chest pain, weakness or fatigue, weight loss, appetite loss, chills, fever and night sweats.
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