∵F1,F2为椭圆C1: x2 a2 + y2 b2 =1(a>b>0)与双曲线C2的公共点左右焦点,△MF1F2是以线段MF1为底边的等腰三角形,且|MF1|=2,∴|MF2|=|F1F2|=2c,∵椭圆C1的离心率e= 3 8 ,∴ 2c 2+2c = 3 8 ,解得c= 3 5 ,∴双曲线C2的离心率e= 2× 3 5 2?2× 3 5 = 3 2 .故选:B.