From the 2004 edition:
Small levels are known to transfer into milk, though they probably pose few problems. In one study of 5 patients, following an 80mg IM dose, tobramycin levels in milk ranged from undetectable to .5 mg/L. Tobramycin is poorly absorbed orally and would be unlikely to produce significant levels in an infant. Lactation risk cat: L3. Adult concerns: Changes in GI flora.
Hope that helps!