Thousands had gathered in Washington DC as Congress voted to formally certify President Joe Biden’s victory over Donald Trump at November’s election.
Mr Hawley and Mr Cruz led objections in the Senate to Mr Biden’s victory, despite the widespread recognition that the effort would fail.
In the end, Congress certified Mr Biden’s Electoral College victory, but not before thousands marched to the Capitol at Mr Trump’s urging, overwhelmed security and interrupted the proceedings.
The violence led to five deaths, injured dozens of police officers and caused extensive damage to the Capitol.
The Democratic senators said the question for the Senate to determine is not whether Mr Cruz and Mr Hawley had the right to object, but whether the senators failed to put loyalty “to the highest moral principles and to country above loyalty to persons, party, or Government department”.
They also said the investigation should determine whether Mr Cruz, of Texas, and Mr Hawley, of Missouri, engaged in “improper conduct reflecting on the Senate”.
“Until then, a cloud of uncertainty will hang over them and over this body,” the Democratic senators wrote in a letter to the leaders of the Senate Ethics Committee.
The Democratic senators said Mr Cruz and Mr Hawley announced their intentions to object even though they knew that claims of election fraud were baseless and had led to threats of violence.
“Their actions lend credence to the insurrectionists’ cause and set the stage for future violence. And both senators used their objections for political fundraising,” the Democratic senators said in their letter.
Both Mr Cruz and Mr Hawley have condemned the violence on January 6, with the former calling it a “despicable act of terrorism”.
Mr Hawley said: “Joe Biden and the Democrats talk about unity but are brazenly trying to silence dissent.
“This latest effort is a flagrant abuse of the Senate ethics process and a flagrant attempt to exact partisan revenge.”
A spokeswoman for Mr Cruz, Maria Jeffrey Reynolds, added: “It is unfortunate that some congressional Democrats are disregarding President Biden’s call for unity and are instead playing political games by filing frivolous ethics complaints against their colleagues.”