Tamiflu appears to be safe for breast feeding babies.

Pregnant Patients: The American College of Gynecology (ACOG) and the Centers for Disease Control and Prevention (CDC) recommend that all pregnant women be vaccinated against the seasonal flu.  Pregnant women may receive the injectable vaccine during any trimester of pregnancy.  However, the live attenuated vaccine known as FluMist is not recommended in any stage of pregnancy. Thimersol is contained in small amounts in the multi-dose vials, but the single dose vials do not contain thimersol. Further, despite certain internet stories, there is no squalene present in any of the influenza vaccines used in the USA.  The seasonal flu vaccine has be administered without major complications to millions of pregnant women throughout the years

Breastfeeding Patients: The CDC and the Food and Drug Administration (FDA) recommend that all breastfeeding women be immunized against the flu.  This will further protect the breastfed infant as these antibodies will pass into milk and help protect the newborn from infection.  Again,  the multi-dose vials contain a small amount of mercury, but there is no evidence that this would even pass to a breastfeeding infant.  The live attenuated vaccine,  FluMist,  is not recommended for breastfeeding women,  although we know the risks are low. 

Treatments

Oseltamivir (Tamiflu) or zanamivir (Relenza) are both quite active against seasonal flu.  These antivirals only work if used early in the illness.  They are not indicated if fever and illness has been present for more than 48 hours.

However, patients should first be evaluated by a physician to see if their fever is due to influenza or perhaps some other infectious agent (bacterial) prior to receiving a prescription for these antiviral agents. 

Pregnant Patients: The antivirals oseltamivir (Tamiflu) and zanamivir (Relenza) can be used in pregnant patients, regardless of trimester of pregnancy, as the risks of influenza are much higher than the risk of these medications.   There are no indications that these drugs harm a fetus.

Breastfeeding Patients: Oseltamivir (Tamiflu) is probably compatible with breastfeeding.  Levels of  oseltamivir in milk (39 ng/mL) are very low and would be subclinical to an infant. The infant would receive only about 0.5% of the mothers dose.  The CDC considers oseltamivir safe to use in breastfeeding mothers.  At present, we do not have breastfeeding data on zanamivir (Relenza).  While it is probably safe to use,  physicians are advised to use oseltamivir (Tamiflu) instead of  zanamivir (Relenza) in breastfeeding mothers.

References

http://www.cdc.gov/flu/protect/vaccine/pregnant.htm

http://www.acog.org/departments/dept_notice.cfm?recno=20&bulletin=5377

Wentges-Van HN, Van EM, Van der Laan JW. Oseltamivir and breastfeeding. Int J Infect Dis. 2008