I believe the CI version of what you want can be found at the link below. Sample size could be an issue as noted in the link. The fact that one incidence rate is 0 should not be a problem. The Full two sample case is treated in Sect 14.3 of Rosner, Fundamentals of Biostatistics, 6th ed. Thompson(Brooks/Cole).  Best wishes.

http://stats.stackexchange.com/questions/37894/comparing-incidence-rates

 Well "incidence" look like "Bernoulli event", I think you should look at chi2 test or poisson test (rare event law) depending of the rate values...

I agree with David, incidence rate of 0 is not really a problem however sample size is.

Regards. 

Please note the latest American Statistical Association article on the interpretation of P values. A good read.

Thank you All! After reading the suggested literature, I think I will got for the chi square test.  I re-did my other sample comparisons (the ones that are non-zero) using the chi-square test and I got the same p values when compared with the z-test. My sample with zero incidence is of similar size as the non-zero samples so I think it will be safe to use the chi square for it. Thanks again!

Just a comment that the Chi-square test on a 2x2 table is comparing the incidence proportions, not the incidence rates.  For more info on the distinction, see the link below.  HTH.

p.s. - The square root of the Chi-square test statistic for you 2x2 table = the z-test value for the usual z-test to compare two independent proportions.  I.e., the two tests are equivalent.

http://sphweb.bumc.bu.edu/otlt/MPH-Modules/EP/EP713_DiseaseFrequency/EP713_DiseaseFrequency4.html