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File package.json:

 "scripts": 
 "test": "tsc --project . --noEmit"
 ,
 "dependencies": 
 "@types/react": "^16.7.6",
 "@types/react-dom": "^16.0.9",
 "react": "^16.6.3",
 "react-dom": "^16.6.3",
 "typescript": "^3.1.6"
 

File tsconfig.json:

 "compilerOptions": 
 "lib": ["es2015", "dom"],
 "target": "es2015",
 "moduleResolution": "node",
 "jsx": "react",
 "strict": true
 

File test.tsx:

import * as React from 'react'
import * as ReactDOM from 'react-dom'
import * as TestUtils from 'react-dom/test-utils'

interface Props 
 a: number


class Component extends React.Component<Props> 
 render () 
 return 'test'
 


const div = TestUtils.renderIntoDocument(
 <div>
 <Component a=1 />
 </div>
) as React.Component

const component = TestUtils.findRenderedComponentWithType(div, Component)

Running tsc --project . --noEmit results with the following error:

src/test.tsx:22:64 - error TS2345: Argument of type 'typeof Component' is not assignable to parameter of type 'ClassType<any, Component, ComponentClass<, any>>'.
 Type 'typeof Component' is not assignable to type 'ComponentClass<, any>'.
 Types of parameters 'props' and 'props' are incompatible.
 Type '' is not assignable to type 'Readonly<Props>'.
 Property 'a' is missing in type ''.

21 const component = TestUtils.findRenderedComponentWithType(div, Component)
 ~~~~~~~~~

Is this a bug? If I disable the --strict option, or omit the <Props> in Component<Props>, it compiles successfully.

The react-dom type declarations were not designed to work when the strictFunctionTypes option is enabled. I have a change to fix the problem you saw and a few others related to strictFunctionTypes. See this answer for the possible ways you can use my modified declarations until they get merged into DefinitelyTyped.