You can just change ground port for your MPU6050 or for your motors(experiment with different choices). You have another ground port near pin13. As far as I know some of them are for analog devices and some of them are for digital (to avoid interference).
Adding capacitors may not help.
If none of the methods will help, try to add an inductor to your circuit.
Please, try that and write here if these were helpful or not.
Update: As per this site the problem is caused by data cables.
Thank you a lot !
Didn't have to change frequency. I just eliminated SDA and SCL wires
and plugged a chip with MPU-6050 directly into Arduino and it works
without any problems. Thanks to you this issue is solved :)
In addition, I would like to mention that Arduino standard pin cables are very noisy, so all connected modules which use high data rates or which are very sensitive to data errors (for example, nRF24L01+) will have strange behavior.
Temporary and harsh workaround: You could reset your Arduino after first initialization process (at the end of setup) then, save a flag("1") to EEPROM so it will not reset each time you start Arduino (warning: EEPROM cells can be rewritten only 10000 times).
//put your reset code here
EEPROM.write(0,0); //make it back "0" for next start