How can I get an ObjectMapper instance in Spring Boot without inheriting from spring-boot-starter-web?

You can add spring-boot-starter-json if you want to avoid to include the full web stack (since Spring Boot v.2.0.0M4).

Why don't you just initialize it yourself.

@Bean
ObjectMapper objectMapper() {
    return new ObjectMapper();
}

You can try and JUST add org.springframework:spring-web dependency as that class is located in it.