You need to disable to internal pull-ups and add a pullup resistor to both, the SDA and the SDL line.
The 20k internal pull-ups are very weak and the usual recommendation is 4.7k. For the 400KHz standard I2C frequency the 4.7k will be fine, for higher frequencies and longer lines things can get more complicated.
As you are connecting a 5V device (the Arduno UNO) to 3.3V device a logic level converter is recommended to prevent damage to th 3.3V device. Adafruit has one or more breadboard ready but be aware that some of these breadboard ready offerings already have pull-ups on board so you don't need any additional ones. Read the spec sheets ;-)
Either way, a pullup resistor is an I2C requirement, it will not work without it.
Here's some reading:
Effects of vrying I2C resistors
Nick Gammons I2C pages,